Home
Class 11
MATHS
Prove the following by using the princip...

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

Text Solution

Verified by Experts

The correct Answer is:
P(n) is true for all natural numbers n.
Promotional Banner

Topper's Solved these Questions

  • 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 :- (2n+7) < (n + 3)^2.

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

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 +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 + 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]

Prove the following by using the principle of mathematical induction for all n in N :- 1^2+3^2+5^2 + ...+(2n-1)^2=(n(2n-1)(2n+1))/3 .

Prove the following by using the principle of mathematical induction for all n in N :- 1.3 + 3.5 + 5.7 +...+ (2n-1)(2n+1)=(n(4n^2 +6n-1))/3

Prove the following by using the principle of mathematical induction for all n in N :- 1.2.3 + 2.3.4 +...+n(n+1)(n+2)=(n(n+1)(n+2)(n+3))/4 .

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 .