Hi I am having alot of trouble with this induction question. Any help would be much appreciated!

Find a formula for 1/1*2 + 1/2*3 + 1/n*(n+1) and prove by induction.

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- February 8th 2009, 07:19 AMvexikedInduction Problem
Hi I am having alot of trouble with this induction question. Any help would be much appreciated!

Find a formula for 1/1*2 + 1/2*3 + 1/n*(n+1) and prove by induction. - February 8th 2009, 07:24 AMrunning-gag
Hi

To find the formula you can compute the first terms of the series.

Another way is to use

- February 8th 2009, 07:33 AMvexiked
So could the formula be

or is this just another way used to solve ?

I can calculate the first few terms but I am not able to find a formula. - February 8th 2009, 07:35 AMrunning-gag
- February 8th 2009, 07:38 AMJester
Here's some details. You'll notice that each term can be split up

Then when you add them up all the terms cancel except the first and last, so

For the induction part, it true for the first few, assume true for

so

Prove true for , i.e.

so

so it must be true for all n. - February 8th 2009, 07:51 AMvexiked
Could you verify that I am on the right track for another?

Prove that 3^n < n! if n is an integer greater than 6..

- Base case 3^7 = 2187 and 7! = 5040

- Inductive

- Assume for p(k) show for p(k+1)

- 3^K+1 < K+1!

- 3^k + 3^k < K + 1!

I am stuck on this part now. - February 8th 2009, 08:25 AMADARSH
You should have an initial condition that n>2

Let the following is true

To prove

Therefore

Putting k! instead of 3^k we get something greater hence if we can prove that this greater thing less than our RHS

then we have done it

For

Thus

and - April 19th 2009, 08:13 PMvexiked
- April 20th 2009, 08:06 AMrunning-gag
danny arrigo already answered to you

What don't you understand ?