Combining power series Use the power series representation

to find the power series for the following functions (centered at 0). Give the interval of convergence of the new series.

f(−4x) = In (1 + 4x)

Solution 32E

Step 1:

In this problem we have to find the power series of f(-4x) = ln(1+4x) (centered at ‘o’), and the interval of convergence of the new series.

Given f(x) = ln(1-x) = - , for -1…………(1)