I'm not sure how to approach these two problems, I've been trying for a couple hours and am getting nowhere. Could someone explain how I'm supposed to solve these?
For each of the following functions f with domain N determine a formula for f(n) and use mathematical induction to prove your conclusion.
1)f(1)=1/2, and for n>1 f(n)=(n-1)(f(n-1)-1/n+1
I've been trying to find an f(n-1) that will make this equality true, but I can't find anyway around the 0 multiplication in the first term, so I must be misunderstanding the problem.
2)f(1)=1 and for n>1 f(n)=(n+1)/3n*(f(n-1))
Any help understanding what this problem is asking for would be greatly appreciated!