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Asked Feb 6, 2020
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2n°
1. Prove that for all positive integers n > 1, the inequality 2" <
<(") holds.
п
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2n° 1. Prove that for all positive integers n > 1, the inequality 2" < <(") holds. п

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Expert Answer

Step 1

Consider the given statement be P(n) as;

Advanced Math homework question answer, step 1, image 1

Apply induction methods to prove the above statement P(n) as follows.

For n=2,

LHS=22=4

RHS

Advanced Math homework question answer, step 1, image 2

Here, 2<6. The statement is true for n=2.

Assume that the given statement is true for some natural number k.

That is,

Advanced Math homework question answer, step 1, image 3

 

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