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

  • Thread starter Grew Gore
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  • #1

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.
 

Answers and Replies

  • #2
andrewkirk
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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?
 

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