Find the sum of the infinite geometric series, if possible.

Question

2 + 16/7 + 128/49 + 1024/343 ...

Answer 1

2 + 16/7 ( 1 + 8/7 + 64/49 + ...)

The content of the parenthesis is 1 + (8/7) + (8/7)^2 + .... which is an infinite geometric series with r > 1.

So the sum diverges.

So the sum of the infinite series is +∞

Answer 2

r = 8 / 7

Series converges only if -1 < r < 1.