Principles of Mathematical Induction

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Principles of Mathematical Induction: Overview

This topic covers concepts such as Principles of Mathematical Induction, Inductive Reasoning (Mathematical Induction), Equivalence with the Well-ordering Principle, Inductive Reasoning Vs Deductive Reasoning, etc.

Important Questions on Principles of Mathematical Induction

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12+22+32+...+n2=?,  nN.

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"Every nonempty subset of natural numbers has a minimal element" is an example for Well-ordering Principle

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34+1516+6364+ upto n  terms is equal to

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If xn-1 is divisible by x-k, then the least positive integral value of k is

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Consider the following two statements :

I. If n is a composite number, then n divides n-1!

II. There are infinitely many natural numbers n such that n3+2n2+n divides n!

Then

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Let Pn be a statement and let PnPn+1 is true for all natural numbers n, then Pn is true

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If 242n+1+33n+1 is divisible by k, k>1 for all n then the value of k is

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If 1.2+2.3+3.4+.+n(n+1)=n(n+1)(n+2)3=P(n), then 

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If  3.6+6.9+9.12+..+3n(3n+3)=3n(n+1)(n+2)=P(n) then 

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For all nN, n(n+1)(n+5) is a multiple of 

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Inequality 3n<(n+1)!, nN

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For all nN,  2.5+5.8+8.11+.+(3n-1)(3n+2)=n3n2+6n+1=P(n) then 

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If we take any three consecutive natural numbers, then the sum of their cubes is always divisible by 

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For every natural number n,  n3+(n+1)3+(n+2)3 is divisible by  

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For all nN, 1·2+2·22+3·23++n·2n=

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For all nN, 1.3+2.32+3.33+..+n.3n=

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The statement :2n>3nnN.

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For all nN72n+23n33n1 is divisible by  

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nN, 6n+2+72n+1 is divisible by