Help Determining which Maclaurin Series to use for this Problem

[student93]

Homework Statement

Problem is attached in this post.

Homework Equations

Problem is attached in this post.

The Attempt at a Solution

I came up with the function (1+x)^1/n and tried to derive a maclaurin series out o fit but to no avail, I can't determine what maclaurin series to use.

 

[lurflurf]

Use the binomial series

 

[xiavatar]

If you haven't already realized it, binomial coefficients can be generalized to take fractional values. Namely

$$\binom{p/q}{m}=\frac{\frac{p}{q}(\frac{p}{q}-1)...(\frac{p}{q}-m+1)}{m!}$$.

And furthermore, note that

$$\binom{p/q}{1}=\frac{p}{q}$$