Prove by induction that

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- Apr 10th 2010, 01:51 AMdifferentiateProve by induction that (3^n + 5^n)/2 >> 4^n
Prove by induction that

Thank you - Apr 10th 2010, 02:46 AMArchie Meade
- Apr 10th 2010, 09:22 AMnovice
Your question is not complete, for which it is required that be defined, since in the case of , the statement

is false, i.e. . So for it to be true ought to be greater than 2.

Since we must prove by induction, we will restate the question correctly. So let for , .

Basis step:

Next is the Inductive step:

We will prove that is true.

So

. We multiply both sides by 2 and obtain

Next, multiply both sides by 3 and obtain

. We now add to both side and obtain

.

Next, we add and subtract to the right hand side and obtain

Since the smallest integer permissible for the basis step is , we substitue 2 for k for the items in the parenthesis and obtain

Now the proof is complete.