Taylor Series for f(x) = (1+x)^m

[Grew Gore]

Homework Statement

i) What is the Taylor Series for f(x) = (1+x)^m about x=0 where m is a real number?
ii) Why does this binomial series terminate when m is a non-negative integer? A
iii) Can the result to (i) be used to find the first four non-zero terms of the series for (1+x)^(-1/2)

Homework Equations

The Attempt at a Solution

I started getting: 1 + mx + 1/2(m-1)mx^2 +1/6(m-2)(m-1)mx^3 +... but am unsure if this is right and how to go on from here.

 

[andrewkirk]

That looks correct for (i) although they may prefer you to use general summation notation rather than '+...'
Now do (ii). Hint: Which, if any, of the terms in the expansion you wrote as answer to (i) will be zero if m is a positive integer?