Converging analysis question

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

And err, I cant seem to do part (iv) and (v), any help will be appreciated, thanks!

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