- #1

Hat1324

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## Homework Statement

The question asks me to prove inductively that 3

^{n}≥ n2

^{n}for all n ≥ 0.

## Homework Equations

## The Attempt at a Solution

I believe the base case is when n = 0, in which case this is true. However, I cannot for the life of me prove n = k+1 when n=k is true. I start with:

[itex] 3^k ≥ k2^k [/itex]

and then try:

[itex] 3^{k+1} ≥ (k+1)2^{k+1}[/itex] which gets me nowhere.

I then try:

[itex] 3^{k+1} ≥ 3k2^k [/itex]

but I still have no idea where to go from there. Please help :(

Whoops the Latex is all whack. Edit: Thanks

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