- #1
Hat1324
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Homework Statement
The question asks me to prove inductively that 3n ≥ n2n 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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