Convergence Write the remainder term Rn (x) for the Taylor series for the following functions centered at the given point a Then show that for all x in the given interval.

f(x) = ln(l + x), a = 0, -

Solution 39RE

Step 1 of 2:

In this problem we need to find the remainder term in the taylor series expansion of f(x) = ln(1 +x) at center a = 0 , and we have to prove that = 0.

Thus the Taylor series of with center 0 is as follows;

Given : f(x) = , then f(0) = = 0 , since

= = , then = = 1

= )= , then = = -1

= = , then = = 2

……………………. ……………(2)

Therefore , the Taylor series of with center 0 is as follows;

…….

ln(1+x) = x - + -...........

=