using mathematical induction...

help please

thank you

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- Nov 30th 2008, 12:27 PMNeedHelp18How to prove that n^2 + n + 2 is even??
using mathematical induction...

help please

thank you - Nov 30th 2008, 12:38 PMrunning-gag
It's a pity to use induction

n²+n+2 = (n+1)² - n + 1

n odd => (n+1)² even => (n+1)² - n + 1 even

n even => (n+1)² odd => (n+1)² - n + 1 even

By induction

Easy for n=0

If right for n then n²+n+2 even

(n+1)²+(n+1)+2 = n²+2n+1 + n + 3 = n²+n+2 +2n+2= n²+n+2 +2(n+1) - Nov 30th 2008, 01:22 PMSoroban
Hello, NeedHelp18!

Quote:

Prove by induction: . is even.

Verify . . . even!

Assume

Add to both sides: .

We have: .

. .

. .

And we have proved . . . The inductive proof is complete.

- Nov 30th 2008, 02:24 PMKrizalid

is odd hence is odd and is even, therefore is even.