mathematical induction questions for class 11

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 Mathematical Induction

1.      Prove by the principal of mathematical induction that for all n ɛ N;

i.          1² + 2² + 3² + ---------- + n² = (1/6) n (n + 1) (2n + 1).

iii.      1 + 2 + 3 + ---------- + n =  n/2 (n + 1)

iv.       1.3+2.4+3.5+ --------- + n.(n+2) =  n/6 (n + 1) (2n + 7).

2.      Prove by the principal of mathematical induction 5²ⁿ – 1 is divisible by 24 for all n ɛ N.

3.      Prove by the principal of mathematical induction 3²ⁿ + 7 is divisible by 8 for all n ɛ N.

4.      Prove using mathematical induction 5²ⁿ⁺² – 24n – 25 is divisible by 576 for all n ɛ N.

5.      Prove by the principal of mathematical induction 2.7ⁿ +3.5ⁿ – 5 is divisible by 24 for all n ɛ N.

6.      Prove by the principal of mathematical induction 4ⁿ +15n – 1 is divisible by 9 for all n ɛ N.

7.      Prove by the principal of mathematical induction 10ⁿ + 3.4ⁿ⁺² +5 is divisible by 9 for all n ɛ N.

8.      Prove by the principal of mathematical induction.....

i.             1 + 2 + 3 + ---------- + n < 1/8  (2n + 1)²

ii.           (2n+7)<(n+3)²

iii.            n < 2ⁿ for all n ɛ N.

iv.              (ab)ⁿ = aⁿbⁿ

9.      Prove that 7ⁿ – 3ⁿ = is divisible by 4.

10.  Prove that 1² + 2² + 3² + ---------- + n² >.

11.  Using principal of M.I. prove that equation is true for all n ɛ N

Cosα. Cos2α.Cos4α.Cos8α……………..Cos(2^n-1α) =

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