Exercise 7.1 Class 11 Maths Mathematical Induction| Ex 7.1 Class 11 KPK Board Mathematical Induction

Exercise 7.1 Class 11 Maths Mathematical Induction| Ex 7.1 Class 11 KPK Board Maths Mathematical Induction | Study With Me
00:09:11 Intro
00:07:18 Q1
00:12:11 Q2
00:16:39 Q3
00:19:41 Q4
00:23:22 Q5
00:27:15 Q6
00:30:34 Q7
00:34:33 Q8
00:35:45 Q9
00:41:38 Q10
00:45:24 Q11
00:48:56 Q12
00:57:09 Q13
01:04:21 Q14
01:15:17 Q15
Establish the formulas given below by mathematical Induction
Q1. 2 + 4 + 6 + . . . + 2n = n(n+1)
Q2. 1 + 5 + 9 + . . . + (4n-3) = n(2n-1)
Q3. 3 + 6 + 9 + . . . + 3n = 3n(n+1) / 2
Q4. 3 + 7 + 11 + . . . + (4n-1) = n(2n+1)
Q5. 13 + 23 + 33 + . . . + n3 = [n(n+1)/2]^2
Q6. 1(1!) + 2(2!) + 3(3!) + . . . + n(n!) = (n+1)! - 1
Q7. 1.2 + 2.3 + 3.4 +...+ n(n+1) = n(n+1)(n+2) / 2
Q8. 1 +2 +22 +23 + . . . + 2n-1 = 2n-1
Q9. 1/3 +1/9 +1/27 + . . . + 1/3n = ½(1 - 1/3n)
Q10. 5C5 + 6C5 + 7C5 +…+ n+4C5 = n+5C6
Q11. 2C2 + 3C2 + 4C2 +…+ nC2 = n+1C3 for n ≥ 2
Q12. Show by mathematical induction that these are integers
(i) (52n - 1)/ 24
(ii) (10n-1 - 9n - 10) / 81
Q13
(i) 2n is greater than n for all n element of N
(ii) n! is greater than n2 for every integer n ≥ 4
Q14
(i) Show that 5 is a factor of 32n-1 + 22n-1 where n is any positive integer
(ii) Prove that 22n-1 is a multiple of 3 for all positive integers
Q15 Show that a + b is a factor of an- bn for all even positive integer n.
Exercise 7.1 Maths Class 11 KPK Book
Exercise 7.1 Maths Class 11 KPK Board
Exercise 7.1 Maths Class 11 Federal Board
Class 11 Mathematical Induction
Exercise 7.1 maths class 11 kpk board book Mathematical Induction Federal Board
Ex 71 maths class 11 kpk board book Mathematical Induction
Ex 7.1 class 11 maths Mathematical Induction kpk book
Class 11 maths ch 7 ex 7.1 Mathematical Induction
Exercise 7.1 class 11 maths Mathematical Induction
Chapter 7 maths class 11 exercise 7.1
Ex 7.1 Questions 1
Ex 7.1 Questions 2
Ex 7.1 Questions 3
Ex 7.1 Questions 4
Ex 7.1 Questions 5
Ex 7.1 Questions 6
Ex 7.1 Questions 7
Ex 7.1 Questions 8
Ex 7.1 Questions 9
Ex 7.1 Questions 10
Ex 7.1 Questions 11
Ex 7.1 Questions 12
Ex 7.1 Questions 13
Ex 7.1 Questions 14
Ex 7.1 Questions 15
Exercise 7.1 Questions 1
Exercise 7.1 Questions 2
Exercise 7.1 Questions 3
Exercise 7.1 Questions 4
Exercise 7.1 Questions 5
Exercise 7.1 Questions 6
Exercise 7.1 Questions 7
Exercise 7.1 Questions 8
Exercise 7.1 Questions 9
Exercise 7.1 Questions 10
Exercise 7.1 Questions 11
Exercise 7.1 Questions 12
Exercise 7.1 Questions 13
Exercise 7.1 Questions 14
Exercise 7.1 Questions 15
Class 11 ex 7.1 solution
Ex 7.1 class 11
Exercise 7.1 Maths Class 11
Exercise 7.1 Class 11 Maths
Exercise 7.1 Class 11 Maths KPK Board
Exercise 7.1 Class 11 Maths KPK Book
#Exercise7.1 #MathsUnit7 #KPKBoard #MathematicalInduction #Class11 #FederalBoard #FBISE #Unit7Exercise7.1 #Ex7.1MathsClass11 #Class11Maths #MathsClass11 #ProveusingMathematicalInduction #ProveanInteger #Hypothesis #Isafactorof #Isamultipleof @studywithmeinpakistan
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[@MuhammadRohanAshraf]

Sirg Improvement ka exam ke lie important chapters pe Video banai please

[@FatimaZahra-p3p]

Assalam o alikum sir i want guidance about maths mcqs 1st year kindly make video for mcqs portion or if you have any material for maths mcqs preparation then kindly share it i shall be very thankful to you

[@StudywithmeinPakistan]

I made two videos on MCQs from SLO based kzbin.info/www/bejne/gImUiKqwe6eAe68si=9tG5k0_n5QrGFEHV And kzbin.info/www/bejne/bpbIe4WDnbpjaassi=y8nBWWsc_Ztb6N1H

[@sportshigh47]

Thanks sir

[@educationshack_]

Outstanding... JazakAllah 😊💎

[@StudywithmeinPakistan]

Welcome

[@MohammadShafay-jf6rb]

Sir you gain another subscriber 🎉❤❤

[@StudywithmeinPakistan]

Welcome boy

[@aleeshairfan6607]

Thank u soo much sir Jazakallah

[@StudywithmeinPakistan]

Welcome bachay

[@salmanwaheed00]

1:04:05 I had a confusion related to this so I searched on chat gpt to clear my doubt. If you also have the same doubt read this below. In mathematics, when dealing with inequalities, you can substitute an expression with an equivalent one as long as the equivalence is based on valid mathematical rules. Now, if you substitute 3^2 with (3+1), you would get (25 > (3+1), which simplifies to (25 > 4). This statement is also true. So, in this particular case, both (25 > 3^2) and (25 > (3+1)) are true statements.

[@pakclubmusic]

aap bhi tayari kar rehay ho papers ki? tayari kesi ja rehi?

[@salmanwaheed00]

@@pakclubmusic yaar Abhi thak sirf 2 chapters hee kiye hain. Lekin inshallah hojayega complete.

[@StudywithmeinPakistan]

Great

[@sarimahmed6389]

you are jacked man

[@salmanwaheed00]

@@sarimahmed6389 thanks dude🖤

[@SurprisedGiraffe-vn7bb]

Assalamualaikum sir hope you are doing well sir I request from you to videos for students who want to give improvement

[@SurprisedGiraffe-vn7bb]

Make*

[@StudywithmeinPakistan]

Beta videos made for main exams are equally good for Improvement. Moreover I will be busy in making 2nd year stuff from here onwards. Regards

[@RajaAbbas-hn1oc]

thanks sir😍

[@StudywithmeinPakistan]

💫

[@Abdullah-v8b7t]

Sir apny english ki grammar ki video bnayi hai. Kindly physics kay conceptual MCQs py bhi video bana dain. Jazak Allah........

[@StudywithmeinPakistan]

Beta abhee to time bohat Kam hay. Aur sir Atif nay us peh shayad already kaam kar rakkha hay.

[@spritelmao]

Sir if time is less then what to do for boards what are important chapters in math

[@StudywithmeinPakistan]

Beta maths mein choice naheen Karni chahiey

[@Sharjeelahmad-bn8ms]

sir hmara computer ka paper last h agr ap usk 1 ya do din phle bhi normalization topic upload kr lete hn to wo ham tyar kr lenge

[@StudywithmeinPakistan]

InshaAllah I will try don't worry. Coz my son will also need that.

[@Sharjeelahmad-bn8ms]

thanks alot

[@sportshigh47]

Yes plz

[@RichRoutes-06]

MashaALLAH Allah kush rakhy

[@StudywithmeinPakistan]

Thx

[@emaanrehan8228]

Aoa sir board k pprs start hein please mcqs ka btayn Kuch .... Mcqs m bht no cutting huty please Kuch guide kren k mcqs kse kren 3rd paper math ka hei federal board

[@StudywithmeinPakistan]

Beta MCQs maths Bananay k liey mujhay Khud bhee poori book Karni paray gee for which time is out now. Pardon for that. But I will make of English shortly.

[@Unknown.22376]

Sir federal board k lie konsi maths ki book pe focus rakhna chaiye kpk ya punjab , Balochistan??

[@MZK-YT]

Kpk book

[@StudywithmeinPakistan]

This year KPK book for 1st year.

[@AhmadAnjum-l5x]

sir can you make anyvideo on the mcqs of maths cause mostly maths main numbers mcqs main hi cut hoty hain

[@StudywithmeinPakistan]

I made one last year of SLO based MCQs check that

[@AhmadAnjum-l5x]

@@StudywithmeinPakistan ok thanks

[@rubab.fatima_110]

Thank you so much sir

[@StudywithmeinPakistan]

Welcome beta 👍

[@AbidAli-cw1yy]

Great ❤

[@StudywithmeinPakistan]

Welcome

[@AbidAli-cw1yy]

Thank you sir g ❤

[@fatimaali9785]

Very helpful

[@StudywithmeinPakistan]

Thanks

[@sadiaintazar]

aoa sir... sir can you plz upload lectures of chapter 4 (sequences and series)

[@StudywithmeinPakistan]

WS. Beta abhee to time naheen bacha. But I intend making a video in which I will give an overview of all these chapters. May be in next 7 to 8 days. But certainly before exams.

[@sadiaintazar]

@@StudywithmeinPakistan yes sir i would really appreciate that... paper se pehly pehly acha hai ... or ye imp bhi hai ....btw thank you sir apki bht achi smjh ati☺

[@ManahilQazi-uu5dl]

Board k lehaz se kon kon se chpters important h

[@StudywithmeinPakistan]

9th seems to me of least Important. Baaki sab Important Hain.

[@AbdulWahab-ic8jt]

​@@StudywithmeinPakistan5th is least important 2 short and 1 long will come from chap 9th

[@StudywithmeinPakistan]

You may leave either 5 or 9th Not both.

[@AbdulWahab-ic8jt]

@@StudywithmeinPakistan yes but leaving 5 is better in my opinion

[@qeetyu4]

❤❤❤

[@StudywithmeinPakistan]

Thx

[@MZainHasanGhori]

This exercise is the most useless and bakwass Exercise . koi logic nae bnti ha . Answer lany ky liye kuch bhi fazol step ho jata ha iss exercise ma

[@StudywithmeinPakistan]

:-)

[@Itxabdul-s9g]

Sir chp no 5 aur 12 karna zaroori hain plz tell bcz many of my friends skip these chapters

[@StudywithmeinPakistan]

If you skip these you have to be 100% perfect in the remaining one's . Moreover you might lose 2 to 4 marks in MCQs too.

[@UmerJutt-j6k]

Assalamualaikum sir, sir ma both confused ho raha hon, sir you tube par sab kahta han ka hama seraf important topic karna chiya laken sir college ma teachers kahte han ka paper ma unimportant bii ata haii , sir ham kis ko follow karenn??

[@StudywithmeinPakistan]

For maths don't leave anything in choice

[@UrdustoriesUrdustories-u9d]

Tention nahi lo bro chill,😊

[@Ender072]

Thank u so much sir, i couldnt understand q12 and q13 before, now i understand tysm

[@StudywithmeinPakistan]

All the best 👍🎁

[@IKhan1436-n6s]

sir q2. mein right side and left side equal nahe hai tu phir ye kese true hai step 3 me

[@Atheist5577]

Assalamualaikum sir. Sir 11 maths Kai model paper ki Tarah important question bataye na.. Guess paper..

[@StudywithmeinPakistan]

Beta Maths mein guess naheen Lena chahiay hay.

[@Atheist5577]

@@StudywithmeinPakistan Nai sir important question and topics according to paper

[@MisbahRashid-wv8vh]

Good morning 🌞

[@StudywithmeinPakistan]

Good Afternoon beta. 👍

[@huda_eva]

Assalamualaikum Sir Kindly make a guess paper of maths 1st year federal board Sir kindly post it in this week. Sir it's a request.

[@StudywithmeinPakistan]

Walaikumussalam G Beta Jaisay he authentic information Milay ge to I will definitely share that.

[@UrdustoriesUrdustories-u9d]

Ok

[@Rajpootfamily-p9q]

Mery sy rabta kro

[@thedoctor_offical]

Sir g 9.2 karwa dein plz WO KZbin pe bohat kam available hai

[@StudywithmeinPakistan]

Beta ab time naheen bacha

[@iammuslim12349]

kzbin.info/www/bejne/moKwfoh3g9usetk

[@Amna_creations]

Really helpful ✨

[@StudywithmeinPakistan]

Welcome

[@MuhammadRohanAshraf]

Sirg q10 aur 11 me combination he kio use hoa Permutation kio nai

[@StudywithmeinPakistan]

This video will clear your concepts on this. kzbin.info/www/bejne/aqiwo3iJfa10rtU

[@ayeshasatti1512]

Sir PATA kese chalyga ga kkab eq A ko b jesa krna or kaha B ko A jesa

[@StudywithmeinPakistan]

Total 2 he type k to sawal Hain beta. Inequality Wala aur integer Wala.

[@FatimaNoor-vg5yn]

Sir mcq bhi upload kryein anaa is lyyy

[@StudywithmeinPakistan]

Maths MCQs preparation Part-1 kzbin.info/www/bejne/gImUiKqwe6eAe68si=2tiUWjgDLkPBnIql Part-2 kzbin.info/www/bejne/bpbIe4WDnbpjaassi=YQclI_dhYkTj4vad

[@thedoctor_offical]

Sir g computer chapter 7 karwa dein one shot please

[@StudywithmeinPakistan]

Beta time naheen mil Raha. 😱

[@thedoctor_offical]

Sir.g ye chapter zaroor karwain bohat mushkil hai jaise normalization

[@Keys876]

Fbise new bpok bhi karwy plz

[@StudywithmeinPakistan]

Beta is saal to mein 2nd year ki cheezein Karwa Raha kiyonkeh my own son is now in 2nd year. I hope you will understand . But I am sure these three exercises will clear your concepts far better than what can be taught in college.

[@generations6342]

SIR KINDLY TELL US IMP MCQS FOR MATH. LAST FIVE YEARS MATHS MCQS ARE FROM OTHER BOARDS NOW OUR MATH BOOK IS OF KPK BOARD KINDLY UPLOAD MCQS FOR KPK BOARD FAST OUR PAPER IS ON SATURDAY. ( FBISE)

[@StudywithmeinPakistan]

Last 5 years k to naheen hain, but these are all i made kzbin.info/www/bejne/aoCnY6uXgbV3qM0si=uB4KXBfcq7v_LUpN kzbin.info/www/bejne/gImUiKqwe6eAe68si=qhlmixKWfJvi6yrg kzbin.info/www/bejne/bpbIe4WDnbpjaassi=xDHF0o8pYYb4Rn7Z

[@AHadiAbbasi]

Sir chp 10 b krwa dein

[@StudywithmeinPakistan]

Beta abhee to time he naheen bacha. I have to do paper to paper few tips.

[@muhammadzohaib-f9t]

29.31 se samag nhi aie common lia one kasie aia

[@uzairtahir-rf1hm]

Sir please ap chp 12 bhi upload kar day

[@StudywithmeinPakistan]

Beta abhee time naheen bacha warnah zaroor karta.

[@iammuslim12349]

you can watch ehtisham tariq for ch 12

[@uzairtahir-rf1hm]

Thank you I will watch it

[@MuhammadSayyam-qe3te]

​@@iammuslim12349 You can watch *maths with easy understanding* for chapter 12

[@Zaraqii333]

1:00:05 sahi Nahi samaj aya sir Akhri Number Ko nahi lekhty???

[@StudywithmeinPakistan]

Beta right side peh mein nay relate karwaya thaa par youn samjhein. Aapko age agar 17 years hay aur aapki aik sister ki 9 yrs aur doosri ki 5 yrs. It means 17 > 9 + 5 true. Aur 17 > 9 will also be true. Hope ab samajh aa gaya Hoga.

[@Annan72]

Sir 2nd year ki maths session ke start se hi shuru kr di jiye choti se break ke badd beacause you deserve break

[@StudywithmeinPakistan]

InshaAllah. Let's hope Book Name gets confirmed. 1st year ki to saari he change ho gae Hain almost.

[@nothingelse222]

Unit 05 are not available

[@StudywithmeinPakistan]

Nops beta. Is saal only 2 chapters he banae hain

[@FatimaNoor-vg5yn]

Ap or subjects ki vedio b tu bna rhy

[@StudywithmeinPakistan]

Beta abhee english k MCQs ki aik video bana Raha. Maths k MCQs Bananay k liey to poori book parhni paray GE coz basically I am a. Physics teacher.

[@FatimaNoor-vg5yn]

@@StudywithmeinPakistan sir ap isi chapter KY krwa dyein bs

[@StudywithmeinPakistan]

@@FatimaNoor-vg5yn Ok InshsaAllah will try before exams.

[@we.are_venom]

Sir uski jaga hamne Q1 kiun likha

[@StudywithmeinPakistan]

Kiski Jagah

[@maheen_fatima]

Sir example 7 aur 6 samhaja dein please!!!!

[@StudywithmeinPakistan]

Leave them. I discussed with concerned authorities. They are poorly solved and won't come either.

[@maheen_fatima]

@@StudywithmeinPakistan okk thank you sir

[@mydrawimgs]

.

[@StudywithmeinPakistan]

Hope your paper went well?

[@Ender072]

59:59 sir aap ne side par jo relate it likha he, woh solution ka hissa he? Aur sir 1:03:24 sidr par jo likha he woh solution ka hissa he?

[@StudywithmeinPakistan]

Naheen beta woh sirf weak students ko samjhanay k liey thaa.

[@Ender072]

Ok sir thanks

[@talalmustafa-vq3om]

sir how many mars your son scored ?

[@StudywithmeinPakistan]

443. Alhamdulillah.

[@MuhammadJibran-m4y]

​@@StudywithmeinPakistan sir ap konsey college mey pardha tey hey or apka beta konsey college mey pardh ta hey??

[@AbdullahAzhar-k8j]

Ending sy smj ni araha jaha sy k+1 add krna 😖😖

[@StudywithmeinPakistan]

Beta 3 to 4 questions kareingay to InshaAllah pattern samajh aa jaega.

[@UrdustoriesUrdustories-u9d]

Mera b yahi msla ha

[@Shortgpts]

But sir in question number 13 the square of 1 is smaller than k+1