Question

2^n+2-2^n+1+2^n÷2^n​

Answer 1

Answer:

n2<2n

P(n) is the statement n2<2n

Claim: For all n>k, where k is any integer, P(n)

(since k is any integer, I assume I have to prove this for positive and negative integers)

So let base case be P(1), and I have to prove P(n) for n≥1 and n<1

P(1) is 12<21 which is clearly true.

Induction hypothesis: k2<2k

Inductive step (k+1)2<2(k+1)

(k+1)2=k2+2k+1

k2+2k+1<2k+2k+1 by inductive hypothesis

Not sure how to proceed. Is my previous intuition that I have to prove this for n≥1 and n<1 correct?

Answer 2

Hope this helps u.......