## nissn Group Title how to find the sum of this? one year ago one year ago

1. awesomeness123 Group Title

sum of wht

2. nissn Group Title

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

3. satellite73 Group Title

break in to two parts and add

4. satellite73 Group Title

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

5. nissn Group Title

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

6. nissn Group Title

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

7. sirm3d Group Title

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. nissn Group Title

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 Group Title

that's right