Determine whether the infinite geometric series converges. If so, find the sum 1/4+1/16+1/64+1/256

Determine whether the infinite geometric series converges. If so, find the sum 1/4+1/16+1/64+1/256.....

The geometric sequence is Given as `1/4` , `1/16` , `1/64` , `1/256` , ...

And the ratio is

r = `\frac{\frac{1}{16}}{\frac{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