Question

1/3+1/9+1/27+1/81... Compute the infinite sum

Answer 1

Answer:

1/3 + 1/9 + 1/27 + 1/81 +.....

= 1/3^1 + 1/3^2 + 1/3^3 + 1/3^4 +....

This expression is a geometric progression in which its common ratio is 1/3.

So, this series will converge to a finite value which will be equal to

= 1/3/1-1/3 = 1/2.

Hope this helps you !