I needed help proving this statement, this is what I have tried so far
Base case:
n=2
5<9 −> True
Inductive step:
Assume that for some k>=2 , (2k)+1<3k show that P(k+1) holds
-> 2^(k+1) + 1
-> 2*(2^k) + 1
-> (1+1)*(2^k) + 1
-> 2^k + 2^k + 1
< 2^k + 3^k
This is where I get stuck I am not sure where to go from there or how to manipulate that to get 3^(k+1)
Any help would be appreciated thank you
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