Induction

**dwsmith** · July 20th 2010, 02:41 PM

Use induction to show that $2|n(n+1)$

$n=1, \ 2|2$

Assume $p(k)$ is true.

$2|(k+1)(k+2)\Rightarrow 2|(k^2+3k+2)$

$2m=k(k+1)$

Now what?

**eumyang** · July 20th 2010, 02:50 PM

Assume $n = k$ is true.
$\Rightarrow 2|(k)(k+1) \Rightarrow k(k + 1) = 2m$

Show true for n = k + 1:
$\begin{aligned} (k + 1)(k + 2) &= k(k + 1) + 2(k + 1) \\ &= 2m + 2(k + 1) \\ &= 2(m + k + 1) \\ &\Rightarrow 2|(k + 1)(k + 2) \end{aligned}$

**Archie Meade** · July 20th 2010, 03:46 PM

Originally Posted by dwsmith

Use induction to show that $2|n(n+1)$

$n=1, \ 2|2$

Assume $p(k)$ is true.

$2|(k+1)(k+2)\Rightarrow 2|(k^2+3k+2)$

$2m=k(k+1)$

Now what?

K or k+1 is even.
Any amount of an even value is even.

Via induction...

P(k)

k(k+1) is even ?

P(k+1)

(k+1)(k+2) is even ?

Try to prove that P(k) being true also causes P(k+1) to be true

Proof

$(k+2)(k+1)=k(k+1)+2(k+1)$

If P(k) is true, then P(k+1) is true as 2(k+1) is a multiple of 2 and so is even.

Thread: Induction

LinkBack

Thread Tools

Display

Induction

Similar Math Help Forum Discussions

Strong induction vs. structural induction?

Induction

Rigorously prove the principle of complete induction from mathematical induction??

Mathemtical Induction Proof (Stuck on induction)

induction

Search Tags