Im trying to learn this stuff, but it is so freaking confusing just reading a book. If I can see it done, then that helps tremendously!

1. Prove by mathematical induction that 2+5+8+...+1/2n(3n+1)

2. Find F(2), F(3), F(4), F(5) if F(n) is defined recursively by F(0)=0, f(1)=1, f(n+1)=f(n)+2f(n-1)+1 for n = 1,2,...

3. A bagel shop has onion bagels, egg bagels, sesame seed bagels and plain bagels. How many ways are there to choose twelve bagels with at least one of each kind?

4. Find the next larger permutation in lexicographic order after the permutation 42837651?

Im still rereading all the chapters trying to make sense of it. If I manage to figure them out before hand, Ill post up my answers.

Thanks in advance!