Question

how to find the sum of this?

Answer 1

sum of wht

Answer 2

\[\sum_{k=1}^{\infty}\left( 2^{-k}+5^{-k+1} \right)\]

Answer 3

break in to two parts and add

Answer 4

first one is
\[\sum_{k=1}^{\infty}\frac{1}{2^k}=1\]

Answer 5

how did you find that? (Haven't done this in a long time)

Answer 6

the sum is 9/4 (after wolframalpha) but I don't know how to find it

Answer 7

the first term is a geometric series with first term 1/2 and ratio 1/2, the second term is a geometric series with first term 1 and ratio 1/5
use the formula \[S=\frac{ a_1 }{ 1-r }\] to find the sum of an infinite geometric series

Answer 8

so then it is s =0.5/(1-0.5)=1 and 1/(1-1/5)=5/4

1+5/4 =9/4

Answer 9

that's right