Induction exercise

**klik11** · December 27th 2011, 09:07 AM

How do I prove that the next expression is true for every natural n that is above 1:
$2^{n-1}(2^n+3^n) > 5^n$

thanks

**Siron** · December 27th 2011, 09:28 AM

What have you tried?
Do you know how induction works?

**klik11** · December 27th 2011, 09:43 AM

n=k:
$2^{k-1}(2^k+3^k) > 5^k$

n=k+1:
$2^k(2^{k+1}+3^{k+1}) > 5^{k+1}$
$2^k x 2^k x 2+2^k x 3^k x 3 > 5^k x 5$

no idea how to continue

**Siron** · December 27th 2011, 10:08 AM

By observation I would start with the given inequality which holds:
$2^{k-1}(2^k+3^k)>5^k$

Multiply both sides with a factor 5 and proceed.

Thread: Induction exercise