Convergence of Analysis: Troubleshooting and Simplification Techniques

[gomes.]

Stuck on part iii, I am not sure what I've done wrong as my answer seems correct! any help wil be appreciated.

And err, I can't seem to do part (iv) and (v), any help will be appreciated, thanks!

 

[micromass]

It seems that you want to show

$$\frac{1-\frac{1}{2r}}{1+\frac{1}{r}}\leq \frac{1}{(1+\frac{1}{r})^{3/2}}$$

This is equivalent to

$$(1-\frac{1}{2r})(1+\frac{1}{r})^{3/2}\leq 1+\frac{1}{r}$$

Try to work this out. Things you could do to simplify this is squaring both terms and multiplying both sides by a suitable power of r.