Question

Find the sum of the following infinite geometric series, if it exists.

one-third plus one-ninth plus one-twenty-seventh + one-eighty-first plus and so on

Answer 1

The sum of an infiinte series exists when the ratio is in the interval (-1,1)

Here the ratio is 1/3, then the sum exists.

The formula for this sum is A / (1 -r); where A is the first term and r is the ratio

Then, the sum is [1/3] / [1 -1/3] = [1/3] / [2/3] = 1/2

Answer: 1/2