Representing functions by power series Identify the functions represented by the following power series.

Solution 52E

Step 1:

In this problem we need to identify the function represented by the power series .

Consider , = ++++.........

= ++++.......... Is an infinite geometric series , here “ first term (a) = x , common ratio (r)= =

We know that a+ar+ Then () = , if |r|< 1 , , if |r| > 1 |

Therefore , ++++.......... is an infinite geometric series, then

= = f(x) .

Therefore , the function f(x) = represented by the power series .