OK, I am stuck on this MI proof of the following:
Define and for , define .
Prove: For .
First prove the base case for n=0. By definition =1. Now show .
This proves the base case.
Now assume . (IHYP)
We need to show that .
I can manipulate the left hand side. What I'm having a problem with is the permutation on the RHS.
I can take the k+1 term out which gives (k+1)! but I'm still left with the sum of . I can factor out but that doesn't seem to make sense either.
Could someone give me a hint on how to get rid of the in the sum?