## 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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Mathematics
20 mins
2022-05-14T11:50:11+00:00
2022-05-14T11:50:11+00:00 2 Answers
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## Answers ( )

Answer:1111111 +11 + 211 + 2111 + 2111 + 21 +11 + 21 + 311 + 21 + 3111 + 21 + 3111 + 21 + 31 +…+11 + 21 + 31 +…+ n11 + 21 + 31 +…+ n111 + 21 + 31 +…+ n111 + 21 + 31 +…+ n1 >11 + 21 + 31 +…+ n1 > n+111 + 21 + 31 +…+ n1 > n+12n11 + 21 + 31 +…+ n1 > n+12n11 + 21 + 31 +…+ n1 > n+12nStep-by-step explanation:esperoterajudadoebonsestudosThe base case is the claim that

which reduces to

which is true.

Assume that the inequality holds for

n=k; thatWe want to show if this is true, then the equality also holds for

n=k+ 1 ; thatBy the induction hypothesis,

Now compare this to the upper bound we seek:

because

in turn because