Binomial series

a. Find the first four nonzero terms of the Taylor series centered at 0 for the given function.

b. Use the first four terms of the series to approximate the given quantity.

; approximate .

Solution 30E

Step 1:

(a).We have to find the first four nonzero terms of the taylor series centered at 0 for the function

ie, we have to find the terms of the maclaurin series for

The maclaurin series of a function

Therefore

Therefore...