Question

How to find the value of infinite series?

Can someone help me please

Answer 1

i hope theres ore specifics coming :)

Answer 2

\[\sum_{k=1}^{\infty}\frac{ 1 }{ 24 }(\frac{ 5 }{ 6 })^{k-1}\]

Answer 3

sorry I forgot to post the equation

Answer 4

split out the constants

Answer 5

how do I do that? is that the two fractions?

Answer 6

youve essentially got:

\[\sum kc^{n-1}\]
\[k\sum c^{n-1}\]
\[k\sum c^{n}c^{-1}\]
\[kc^{-1}\sum c^{n}\]

Answer 7

split out the constant and then it becomes a simple geometric series

Answer 8

okay so will the number I plug into be k and the fraction be c?

Answer 9

k and c are just generics i pulled out of thin air to fill in the places

Answer 10

other than that, its your exact setup

Answer 11

say; k=1/24 and c=5/6

Answer 12

okay I want to try it really quick

Answer 13

do you remember the formula for an infinte geometric series?

Answer 14

thats when you plug in numbers right?

Answer 15

um, there is a general formula for geometric series that would be used to finish the summation

Answer 16

this one?