## anonymous 4 years ago how to find the sum of this?

1. anonymous

sum of wht

2. anonymous

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

3. anonymous

break in to two parts and add

4. anonymous

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

5. anonymous

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

6. anonymous

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

7. sirm3d

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

8. anonymous

so then it is s =0.5/(1-0.5)=1 and 1/(1-1/5)=5/4 1+5/4 =9/4

9. sirm3d

that's right