Question

help finding sum of series

Answer 1

its supposed to match ar^(n-1)

Answer 2

one question, will the sum be exact or approximate ?

Answer 3

its 12

Answer 4

-:( the number of terms is ∞

Answer 5

what type of series is this drbgonzal ? that will help you figure out how to approach it.

Answer 6

yeah but you find where they converge

Answer 7

Right, the answer is 12 and the series converges on that value. Are you needing help on knowing why? or just wanted to check your answers?

Answer 8

i need to know why

Answer 9

So, do you know what type of series this is?

Answer 10

like alternating, or geometric or taylor series?

Answer 11

it says infinite series

Answer 12

Yes, it is. But there are different types, so in this case it is a geometric series (you perhaps havent heard of the others)

Answer 13

ive heard of some of them but i included ar^(n-1)

but didn't know what to call it because of n+1

Answer 14

geometric series are structured like this:
\[\sum_{n=1}^{\infty}ar^n=a+ar+ar^2+ar^3...ar^n+ar^{n+1}\]
and converges if \(|r|<1\) then it converges to
\[\frac{a}{1-r}\]
in this case:
\[\sum_{n=0}^{\infty}\frac{4^{n+1}}{6^n}=-4*3^{-m} (2^{m+1}-3^{m+1})\]
So:it converges and it does it at 12

Answer 15

thnx