Converging and Diverging Sequences Using Limits - Practice Problems

This calculus video tutorial provides a basic introduction into converging and diverging sequences using limits. It explains how to write out the first four terms of a sequence and how to determine if a sequence converges or diverges by finding the limit of a sequence. If the limit exists and it equals to some constant L as n approaches infinity, then the sequence converges. If the limit does not exist or increases or decreases without bound, that is, to positive or negative infinity - then the sequence diverges. This video contains plenty of examples and practice problems of determining if a sequence is convergent or divergent using Lhopital's rule, the squeeze theorem, and properties of logarithms. It contains example problems with trigonometric functions such as sine and cosine, natural logarithms, square root functions, factorials, and exponential functions.
Improper Integrals: • Improper Integrals - C...
Converging & Diverging Sequences:
• Converging and Divergi...
Monotonic & Bounded Sequences:
• Monotonic Sequences an...
Absolute Value Theorem - Sequences:
• Absolute Value Theorem...
Squeeze Theorem - Sequences:
• Squeeze Theorem For Se...
________________________________
Geometric Series & Sequences:
• Geometric Series and G...
Introduction to Series - Convergence:
• Convergence and Diverg...
Divergence Test For Series:
• Divergence Test For Se...
Harmonic Series:
• Harmonic Series
Telescoping Series:
• Telescoping Series
__________________________________
Integral Test For Divergence:
• Calculus 2 - Integral ...
Remainder Estimate - Integral Test:
• Remainder Estimate For...
P-Series:
• P-series
Direct Comparison Test:
• Direct Comparison Test...
Limit Comparison Test:
• Limit Comparison Test
___________________________________
Calculus Final Exam and Video Playlists:
www.video-tuto...
Full-Length Videos and Worksheets:
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[@TheOrganicChemistryTutor]

Final Exams and Video Playlists: www.video-tutor.net/ Full-Length Videos & Worksheets: www.patreon.com/MathScienceTutor/collections Next Video: kzbin.info/www/bejne/qnncZIeOor-jfJI

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@@theadel8591 I feel like that'll be the case for us, except I bet most of it is going to be power series

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[@horrornight8240]

Yes it is cause the lim as n>infinity of ln(1+(1/n))/(1/n) is ln(1+0)/(0) which is undefined.

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Professor Organic Chemistry Tutor, thank you for using multiple well-known examples to explain/analyze Converging and Diverging Sequences in Calculus Two. In all Calculus textbooks, there is a whole chapter on Sequences and Series. This is an error free video/lecture on KZbin TV with the Organic Chemistry Tutor.

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[@mynameisgrand8937]

At 4:30 why do you multiply the top and bottom by 1/n? How do I recognize when to use this?

[@FerghusCameron]

Did you find out the reason? I just started Pre calculus and would like to know thr proof for multiplying the top and bottom by 1/2

[@hungry3166]

​@@FerghusCameron Just to take the n to an easier place. This can be solved by many ways, and you can keep the n and evaluate it to find the answer (if it's converging or diverging) but dividing by 1/n takes the n to 5/n which leads to the final answer easily (because of the rule 1/n=0).

[@ermiastadesse7042]

why do u use l'hopital rule insted of just substitute infinity in the equation lim n-> infinity n * sin(1/n)??? and all your video are just unreal. u made life easy for us.

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[@cyberzod99]

This is very explanatory. Thanks!

[@RA-pu9jo]

for anyone else scratching there head at this! plugging in inf into (1+1/n)^n = (1+1/inf)^inf = (1+0)^inf = (1)^inf = 1^inf = undefined this is why we had to solve it

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why would you add the last step at 22:15? 1/(n+2) is just 1/infinity which is zero. Absolutely no need to multiply top and bottom to get the zero in the numerator

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[@mansafabrar6872]

Will give u a good idea about convergence nd divergence. But formaly the idea of Convergence nd divergence is different.

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Your videos are great! Thank you. I wonder if someone could help me understand why there is a vertical asymptote at 5/3? Confused!!!

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Watching this 20 minutes before my final

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[@imbored5951]

What should you do if it goes to 0 with infinity but its limit for negative infinity is infinite? Does it till converge?

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[@Blockwise2]

Should not we apply stolz-cesara instead of l’hospital when dealing with sequences? Please explain!

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[@masterofdisaster1911]

7:10 even though it seems counter-intuitive it is technically a continuous function given the ε-δ definition of continuous functions.

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[@vestia8444]

for the question at 13:44 couldn't you just simplify sin(n)/n to 1? Is that an identity that can be used?

[@SiphokaziSithole-qy9nn]

How do you know when to use l'hostital and when to use squeeze theorem?

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Thank you!

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Great video

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[@TaongaPhiri-vn9xq]

Can we also prove by definition of the converging sequence?

[@keLv_dGeneRAL]

as for the case lim as n approaches ∞ of sin(n), why don't we apply lim as n approaches ∞ of |sin(n)|?

[@Rynbrurl]

Sir i am not able to draw graph which u drawing in this lecture Which video can help to drawing graph

[@kelvinlikollari1576]

really helpful, thanks again

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Thanks so much

[@parysmonique]

I thought you couldn’t use the divergence test to determine convergence, only divergent if it doesn’t equal 0.....?

[@ibrahimndiaye340]

I think that’s for series not sequences

[@madlad1.]

In calc 1 and heard that lots of students struggle with series in calc 2, after watching this I’m kinda confused as to why, complicated integration by parts problems seem more difficult.

[@TheBobbyBoucher]

This video is about sequences, not series. Integration by parts is generally easy because it just adds an extra step or two from the basic integration rules since it's the first new technique taught in Calc 2.

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Sir can you explain cauchy's theorem of sequence...plz🙏🙏🙏🙏

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[@mwenge6355]

SOMEONE PLEASE RESPOND!!! Why do we use L'Hopital's rule on n*sin(1/n). Why not just substitute???

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There is no playlist on Sequences. Please make more videos on Sequences

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[@emmanueloseikwame4560]

With the question using the roots why didn't the roots cancel out since you were multiplying both roots?

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Watching while the online exam

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[@zikondenyirenda]

for the last example why do we have to take the natural log? if we use log to any base the answer will be that same base.

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Thanks

[@starrypeaceb]

29:20 Am I missing something? The n-th term test specifically states that if the limit is a real, non-zero number, the infinite sum of the series diverges.

[@nathanyao3525]

I think you're thinking about series instead of sequences.

[@ieatdice-gy8vw]

For the n sin(1/n) example about 17 minutes in why cant you use the properties of imfinity and plug it in for n like all the other problems? Why are we all pf the sudden using lhospitals rule there was not explanation on that

[@StarryCranberry]

I was looking for someone who asked that

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Did you ever find out?

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Nice video

[@collinpowell5412]

5 yrs later I'm here