## zmudz one year ago what is the infinite sum of 1/7 + 2/7^2 + 1/7^3 + 2/7^4+....? thanks

1. anonymous

$\left\{ \frac{ 1 }{ 7 }+\frac{ 2 }{ 7^2 } \right\}+\left\{ \frac{ 1 }{ 7^3 }+\frac{ 2 }{ 7^4 } \right\}+....$ $=\left( \frac{ 7+2 }{ 7^2 } \right)+\left( \frac{ 7+2 }{ 7^4 } \right)+...$ $=\frac{ 9 }{ 7^2 }+\frac{ 9 }{ 7^4 }+\frac{ 9 }{ 7^6 }+...$ $=\frac{ 9 }{ 7^2 }\left\{ 1+\frac{ 1 }{ 7^2 }+\frac{ 1 }{ 7^4}+... \right\}$ $=\frac{ 9 }{ 7^2 }*\frac{ 1 }{ 1-7^2 }=?$

2. zmudz

3/784?

3. zmudz

wait, no, sorry, flipped the denominator for the second fraction. but that makes a negative number....

4. anonymous

correction$=\frac{ 9 }{ 7^2 }\left\{ \frac{ 1 }{ 1-\frac{ 1 }{ 7^2 } } \right\}$

5. zmudz

thanks!

6. anonymous

yw