Mathematics: Prove 2^n n for all n equal to or greater than 1. i mostly need with how to solve the problem when it is greater than rather than equal to. for the

Prove 2^n n for all n equal to or greater than

hoperodriguez3111

04.01.2022

is an integer, you can use induction. First show the inequality holds for n=1

. You have 2^1=21

, which is true.

Now assume this holds in general for n=k

, i.e. that 2^kk

. We want to prove the statement then must hold for n=k+1

.

Because 2^kk

, you have

$2^{k+1}=2\times2^k2k$

and this must be greater than k+1

for the statement to be true, so we require

2kk+1

for

. Well this is obviously true, because solving the inequality gives $3k1\implies k\dfrac13$ . So you're done.

If you

is any real number, you can use derivatives to show that 2^n

increases monotonically and faster than

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andrewbao999

14.03.2022

Step-by-step explanation:

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