Solve the recurrence relation

with the initial condition , and verify your solution by induction on n.

Printable View

- Oct 13th 2010, 04:46 PMnurdynikRecurrence relation
Solve the recurrence relation

with the initial condition , and verify your solution by induction on n. - Oct 14th 2010, 08:07 AMHugal
Didn't you forget some ? :/

'Cause your relation is true just for no matter the value of

Hugal - Oct 16th 2010, 02:42 AMHugal
Ok ! I got what you meant. It is :

right ?

So, now just try to figure out what the first terms of this sequence are.

Try to find and you'll have quite a good idea of what actually the sequence is.

After that, you'll have to prove this. Induction is an easy way to make it.

Good luck,

Hugal - Oct 16th 2010, 05:16 AMPlato
- Oct 16th 2010, 06:26 AMchisigma
- Oct 16th 2010, 06:39 AMSoroban
Hello, nurdynik!

Quote:

Solve the recurrence relation: .

and verify your solution by induction on

Crank out the first few terms and you may see a pattern.

. .

We see that the terms of the sequence are squares,

. . not every consecutive square,

. . but squares of certain numbers.

. .

These are the squares of Triangular Numbers, starting with