Geometric Series

This video introduces geometric series.
mathispower4u.y...

[@Mathispower4u]

The first partial sum starts a1*r0, so there are still n terms there. 0 to n-1 would be n terms. I hope that helps. It is just convenient to start and end the partial sum this way to show the formula. I'm glad you find the videos helpful.

[@Mathispower4u]

That is correct. This formula only works with geometric series when subsequent terms have a common ratio. That is what it means to be a geometric series.

[@ciaralopez9285]

This video was GREAT!!! I was absent from school and watched this and understood it better than I would at school. Thank you so much. I shared the link with my classmates who needed help and they understood it too. You were a great help!

[@Rents-Ch]

ew

[@Mathispower4u]

I do show the harmonic series in the video entitled "The Integral Test".

[@jmich7]

All of the quotes are amazing, too.

[@billbitt96]

I had the exact same question from my new recent math teacher in 2012 and she had the same answer back to me. But in reality we deal with sequences which repeat in patterns more often and not spaced evening between every single term. My math major in 1985 never taught me this geometric sequence, oddly enough and we did get into other more complex sequences in 1985. To each his own. This is just a simple clinical type of problem and not real world at all. It's here to fail students on exams.

[@Mathispower4u]

@mgunar I have another video on infinite geometric series. I'll send it to you.

[@LT72884]

So my question is this. WHY do they multiply by r in the first place. I mean i can follow the derivation just fine but why did they decide(they as in the creator of calculus) to multiply by r. what is that r actually representing??

[@PJ-lr3lh]

r is the common ratio for the Ns. To determine the common ratio, divide the second term with the first term.

[@ski8260]

Common ratio i think?

[@spoiledyt9382]

it is the common ratio lol.

[@lu-gc7gm]

you explain things very simply ty so much

[@AmbulateandNavigate]

Thanks for the video, however your formula for finding the common ratio does not work for all series. For instance series like 3/4+5/36+7/144+9/400 produce different common ratio

[@mariannafeuillet6027]

Help! In the last example why does he do 3^5 instead of 3^5-1 (3^4) which is what the formula states?????

[@AmbulateandNavigate]

oh thanks for the reply. I figured it out, between can you upload videos about telescope sum of a series?

[@math0rama]

Love your video! What software do you use to write in colors on top of your slides?

[@curly0117]

how do you find "r" in a problem where you are only told the "Sn" and a1 and a3???

[@lonababery]

so is this diverges or converges?

[@shibirui11]

Really helps. Thanks

[@mjwenceslao8201]

how did you get the 2 power of 9?

[@mgunar]

What happens if n = infinity? Or is the formula just useful for a geometric series with a finite number of terms.

[@HORROR4EVER]

wouldn’t the sum just be infinity? Lmao I might be a little late

[@superredlion123]

You're a saint. Thank you

[@jayspenh]

How come you do not have Harmonic Series on your website?

[@PoHazard]

this video was so helpful! i really got it. thanks for making this

[@delonge5000]

is there any difference between your sn and sn=first term/1-ratio?

[@zaidobaid3691]

can i know to to find r from sigma and a1?

[@mmastar14]

How do i use a formula for this

[@sean-kv4hp]

What if the first term isn't given

[@iqrasheikh4379]

Sir please can you clear me that how the 9 =n_1 comes here?

[@carmelaisabella4533]

iqra sheikh exponential equation

[@MrPwnedable]

This video really helped! Thanks!

[@johnhurley8918]

What does 'r' represent in the equation. You're biggest mistake is that you never state what each variable in the equation mean. Granted, we can reasonably guess some of them, like 'Sn' being the sum of the first 'n' terms, and 'a1' being the first term in the series, but it is never made clear what 'r' represents.

[@johnhurley8918]

Tommy Davies I know that now, because I watched a different video.

[@frede1905]

John Hurley r stands for "ratio", r is the ratio between any term and the previous term:r=a_5/a_4=a_99999/a_99998=a_6548/a_6547. No matter what number we're dividing, it's always going to be r if the second term is the previous one. That's because a geometric series is a series where the next term in the sequence is the last term times some constant number, and r is this number.

[@sakunthala1291]

Thank you so much

[@enjoyablesounds]

great work!

[@jksdfgyjfhgud]

You sir are a boss!

[@MrBlash93]

Thx u sir . Extremely helpful

[@cptoscar]

By the way, thanks bullcleo :)

[@zin6076]

Thank you!

[@bobthe28th17]

Pepega ( ͡• ͜ʖ ͡• )

[@T_man2143]

Fuck you

[@derekq8790]

@@T_man2143 bites the dust

[@najehmchirgui7968]

Thanks you so much

[@th999ss]

thanks......

[@sh4673r]

thank u

[@carmelaisabella4533]

Why 3069?? When the given last term is 1536??

[@ThisGurlisWeirdd]

i have exam abt this sucks im so dumb

[@cptoscar]

math in 720p , what more can a man beg for?

[@stevenscottoddballz]

5:48 You have the value of n, which is 5. Why isn't that just plugged into the equation to get the answer of 1296?

[@Mathispower4u]

That would only give us the fifth term, a_5. We are looking for the sum of the first 5 terms.