Question

calculus- How do I find the sum of the geometric series?

Answer 1

i think there's a formula for that

Answer 2

hmm sum of a geometric sequence? serie? sounds more like precalc

Answer 3

\[\sum_{n=0}^{\infty}\frac{ 3^n }{ 4^{2n+1} }\]

Answer 4

woooww... i feel sooo old, i used to be good at this, i've forgotten so many things

Answer 5

look google found it ;) :D
https://encrypted.google.com/#safe=off&q=finding%20sum%20of%20geometric%20series
first result lol

Answer 6

har har har

Answer 7

try to right the thing that is getting summed as something times (3/4)^n
use law of exponents

Answer 8

actually it would be more like something times (3/4^2)^n

Answer 9

does r = 3/4 ?

Answer 10

almost
try using law of exponents to write this as something times (another something)^n

Answer 11

here I will give my first step
\[\frac{3^n}{4^{2n}4}\]

Answer 12

im not sure...

Answer 13

\[\frac{1}{4} (\frac{3}{4^2})^n\]

Answer 14

\(\bf \sum\limits_{n=0}^{\infty}\ a_1\cdot r^i\implies \cfrac{a_1}{1-r}
\\ \quad \\ \quad \\
\cfrac{3^n}{4^n\cdot 4^1}\implies \cfrac{3^n}{4^n\cdot 4^n\cdot 4}\implies
\cfrac{1}{4}\left[ \cfrac{3^n}{4^{2n}} \right]\implies
\cfrac{1}{4}\left[ \cfrac{3}{4^2} \right]^n\)

Answer 15

then.. .just ge the 1st term
and use the \(\Large \sum\limits_{n=0}^{\infty}\ a_1\cdot r^i\implies \cfrac{a_1}{1-r}\) equation for it

Answer 16

is the answer
\[\frac{ 1 }{ 4}\times (\frac{ 3 }{ 16 })^0\times \frac{ 1 }{ 1-\frac{ 3 }{16} }\]

Answer 17

well... 1 is not the 1st term is not 1 though :)

Answer 18

oh..i just entered it on my hw and it said its correct

Answer 19

ohhh hmmm I misread you... didn't see the left-side part.... which will make the first term 1/4 :)

Answer 20

ah ok thank you! :)

Answer 21

but basically \(\Large {
\sum\limits_{n=0}^{\infty}\ a_1\cdot r^i\implies \cfrac{a_1}{1-r}
\\ \quad \\ \quad \\
\sum\limits_{n=0}^{\infty}\ \cfrac{3^n}{4^{2n+1}}\implies
\sum\limits_{n=0}^{\infty}\ \cfrac{1}{4}\left[ \cfrac{3}{4^2} \right]^n\implies \cfrac{\frac{1}{4}}{1-\frac{3}{16}}\
}\)

yes

Answer 22

thank you

Answer 23

thank you @freckles

Answer 24

np