Series to functions Find the function represented by the following series and find the interval of convergence of the series.

Solution 53EStep 1:In this problem we have to find the function represented by the series and also we have to find the interval of convergence of the series . = 1+ +++................ Is an infinite geometric series and use the formula for a geometric series. That is , with |r| < 1Therefore , = , for || < 1 ( Since = , for | < 1) = = for || < 1Thus the function represented by the power series is