NCERT Grade 11-Principle of Mathematical Induction-Questions

NCERT Solutions for Class 11 Maths

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Principle of Mathematical Induction

Prove the following by using the principle of mathematical induction for all n ∈ N:

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8.    1.2 + 2.22 + 3.23 + ………….. + n.2n = (n – 1)2n + 1 + 2

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19.   n(n + 1) (n + 5) is a multiple of 3.

20.   102n – 1 + 1 is divisible by 11.

21.   x2n – y2n is divisible by (x + y)

22.   32n+2 – 8n – 9 is divisible by 8.

23.   41n – 14n is a multiple of 27.

24.   (2n + 7) < (n + 3)2

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