Use the hint
so
.
Now integrate the last term.
between limits 0 and 1.
Writing , show this sequence satisfies .
Now, I can't quite get a foothold into this puzzle. I'm thinking there's a simple logical step but I don't see it. Can someone help please? I wanted to try induction but I don't see how I'm supposed to use the idea they've told me to do so. It is required of the problem to use this hint.