Prove the following by using the princip...

Prove the following by using the principle of mathematical induction for all `n in N` :- `41^n- 14^n` is a multiple of 27.

Verified by Experts

The correct Answer is:

P(n) is true for all natural numbers n.

PRINCIPLE OF MATHEMATICAL INDUCTION
OMEGA PUBLICATION|Exercise Multiple Choice Questions|10 Videos
PERMUTATIONS AND COMBINATIONS
OMEGA PUBLICATION|Exercise Multiple Choice Questions (MCQs)|21 Videos
PROBABILITY
OMEGA PUBLICATION|Exercise Multiple Choice Questions (MCQs) |15 Videos

Similar Questions

Explore conceptually related problems

Prove the following by using the principle of mathematical induction for all n in N :- n(n +1) (n + 5) is a multiple of 3.

Prove the following by using the principle of mathematical induction for all n in N :- (2n+7) < (n + 3)^2.

Prove the following by using the principle of mathematical induction for all n in N :- 10^(2n-1) + 1 is divisible by 11.

Prove the following by using the principle of mathematical induction for all n in N :- x^(2n)-y^(2n) is divisible by x + y .

Prove the following by using the principle of mathematical induction for all n in N :- 3^(2n+2)-8n -9 is divisible by 8.

Prove the following by using the principle of mathematical induction for all n in N :- 1/2+1/4+1/8+...+1/2^n=1-1/2^n .

Prove the following by using the principle of mathematical induction for all n in N :- 1 +2 + 3 +...+n < 1/8(2n+1)^2 .

Prove the following by using the principle of mathematical induction for all n in N :- 1.3 + 2.3^2 + 3.3^3 +... + n.3^n =((2n-1)3^(n+1) +3)/4 .

Prove the following by using the principle of mathematical induction for all n in N :- 1^3 + 2^3 + 3^3 + ... +n^3 =((n(n+1))/2)^2 .

Prove the following by using the principle of mathematical induction for all n in N :- 1.2 + 2.3 + 3.4 +... +n.(n+1)=[(n(n+1)(n+2))/3]