Determine whether the infinite geometric series converges. If so, find the sum

1/4+1/16+1/64+1/256....

2 answers

The geometric sequence is
1/4 , 1/16 , 1/64 , 1/256 , ...
And the ratio is
r = 1/16 / (1/4) = 1/4

This infinite geometric sequence converges because the ratio is in the range of -1 < r < 1.

Getting the sum, we use the formula,
S = a1 / 1 - r
S = 1/4 / (1 - (1/4))
S = 1/4 / (3/4)
S = 1/3

Hope this helps~ `u`
Thank you!