Submitted by Anonymous (not verified) on
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I have done the first two parts and I am now attempting the third part of (i):
Show also, for $n\ge1$, that
$$I_n=\frac{n}{n+1}\int_{0}^{1}x^{n-1}(1-x)^{n+1}dx$$
Would a proof by induction be allowed here? Or would that only prove it for integers $n\ge1$ rather than all $n\ge1$? Otherwise could I have a hint?
Induction not needed in (i)
Submitted by cxm on
To show the third part you need to integrate $I_n$ as given at the start of the question by parts.