Joe

Ok, here's the sum.

(7^4) - (7^5) + (7^6) - ... + ((-1)^k) * (7^k) where k is in the set of intergers and k>=4.

All the examples in my book are too different to be of much help to me and I've never done geometric sequence before. Thanks in advance!

Use mathematical induction to give a proof that 3^n < (n+2)! for each integer n>=0.

So far I have:

3^k < (k+2)! is true for 0.

For k+1, 3^(k+1) < (k+3).

Kind of at a loss on where to go next.

Thanks for any help!

First time doing mathematical induction. Any help is appreciated.

Use mathematical induction to give a careful proof that

2+8+14+....+(6n+2)=(n+1)(3n+2) for all intergers n>=1.

r and s are in the set of real numbers. If r is irrational and s is rational, then r/s is irrational. I need to prove this by contradiction. I have a working proof, however I don't think my contradiction is in the right format. Thanks!

I need to prove this by contradiction. I'm not completely sure what the contradiction of this statement is. Thanks!