Question

what is the infinite sum of 1/7 + 2/7^2 + 1/7^3 + 2/7^4+....? thanks

Answer 1

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

Answer 2

3/784?

Answer 3

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

Answer 4

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

Answer 5

thanks!

Answer 6

yw