Find a formula for a recursion by induction

[Guest]

Hi!

I have a recursive formula like this:

a0 = 0
a3 = 1
a4 = 3
a5 = 6
a6 = 10
an+1 = an + (n-1) n >= 3

I need to find a formula for this recursion and prove it by induction. How would i do this?

 

[TchrWill]

........1......2......3......4......5.....
n......3......4......5......6......7
Tn....1......3......6.....10.....15 = the triangular numbers/

Triangular number derive from Tn = n(n + 1)/2.

To make use of your n values of 3, 4, 5, 6, etc., we must rewrite the formula as

Tn = (n - 2)(n - 2 + 1)/2 = (n^2 - 3n + 2)/2.

 

[Guest]

Hi thanks thats, about as far as I too have gotten with the problem. The main issue is that I need to prove the formula by induction this is where im lost. What are the steps necessary to prove something by induction?

Thanks again for your help.

 

[stapel]

I'm afraid we cannot teach classes here, so, to find lessons on induction, try Google.

Eliz.