SOLUTION: Find the sum of the infinite geometric series: 1 + 3/5 + 9/25 + ..., if it exists. Thanks

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The sum of the first 'n'-terms of a geometric series: a, ar, ,,........., is given by when .

When 'n' is very large, << 1 [means is very very less than 1].
So, obviously when 'n' is infinity, << 1 so it can be neglected (means taken as 0) in comparison to 1.
Thus the summation formula for n = becomes

or

Here, a = 1 and so .
Hence the formula of summation of geometric series for infinite number of terms (n -> ) is applicable.

Thus the summation of the given infinite geometric series is

or
or

Hence, the summation of the given series exists and its value is 2.5.