## Given that ‘n’ is any natural numbers greater than or equal 2. Prove the following Inequality with Mathematical Induction [tex] \displa

Question

Given that ‘n’ is any natural numbers greater than or equal 2. Prove the following Inequality with Mathematical Induction

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20 mins 2022-05-14T11:50:11+00:00 2 Answers 0 views 0

1

11

11

11 +

11 + 2

11 + 21

11 + 21

11 + 21 +

11 + 21 + 3

11 + 21 + 31

11 + 21 + 31

11 + 21 + 31 +…+

11 + 21 + 31 +…+ n

11 + 21 + 31 +…+ n1

11 + 21 + 31 +…+ n1

11 + 21 + 31 +…+ n1 >

11 + 21 + 31 +…+ n1 > n+1

11 + 21 + 31 +…+ n1 > n+12n

11 + 21 + 31 +…+ n1 > n+12n

11 + 21 + 31 +…+ n1 > n+12n

Step-by-step explanation:

espero ter ajudado e bons estudos

2. The base case is the claim that

which reduces to

which is true.

Assume that the inequality holds for n = k ; that

We want to show if this is true, then the equality also holds for n = k + 1 ; that

By the induction hypothesis,

Now compare this to the upper bound we seek:

because

in turn because