Algebra

Evaluate the infinite geometric series: 1 + 2/7 + 4/49 + 8/343 + ...     

Well, I see  (²/₇)⁰  +  (²/₇)¹  +  (²/₇)²  +  (²/₇)³  +  ^{. . .} 

but I don't know what to do after that.   

Hello Guest,

Evaluate the infinite geometric series: 1 + 2/7 + 4/49 + 8/343 + ...

${\color{red}Solution:}$

$1 + \frac{2}{7} + \frac {4}{49} + \frac {8}{343} + \mbox { } ...$

$\mathcal{ \mbox {Like Guest said it right } } \mbox { } (^2/_7)^0 + (^2/_7)^1 + (^2/_7)^2 + (^2/_7)^3 + \mbox { } ...$

Use the double summation sign $\sum$ .

$\displaystyle\sum_{n=1}^{\infty} \Bigl( \frac {7}{2} \Bigr)^{1 - n} = \frac {7}{5} = 1.4$ .

$\mathit{ Straight}$