Principle of Mathematical Induction

If n∈N, then 11ⁿ⁺²+12²ⁿ⁺¹ is divisible by
1. 133
2. 132
3. 131
4. None
If n is a positive integer, then 2.4²ⁿ⁺¹+3³ⁿ⁺¹ is divisible by:
1. 10
2. 11
3. 12
4. 13
For all n ≥ 1,
1² + 2² + 3² + 4² +…+ n² =
1. [n(n+1)(2n+1)]/2
2. n/(n+1)
3. [n(n+1)/2]²
4. None
For all n ≥ 1, 1 + 3 + 3² + ... + 3ⁿ⁻¹=
1. [n(n+1)(2n+1)]/2
2. n/(n+1)
3. [n(n+1)/2]²
4. (3ⁿ-1)/2
For all n ∈ N ,1³ + 2³ + 3³ + … +n³ =
1. [n(n+1)(2n+1)]/2
2. n/(n+1)
3. [n(n+1)/2]²
4. (3ⁿ-1)/2
For all n ∈ N ,1.2.3 + 2.3.4 +…+ n(n+1) (n+2) =
1. [n(n+1)(n+2)(n+3)]/4
2. n/(n+1)
3. [n(n+1)/2]²
4. (3ⁿ-1)/2
For all n ∈ N ,1.3 + 2.3² + 3.3³ +…+ n.3ⁿ =
1. [n(n+1)(2n+1)]/2
2. [(2n-1)3ⁿ⁺¹+3]/4
3. [n(n+1)/2]²
4. (3ⁿ-1)/2
For all n ∈ N ,1.2 + 2.3 + 3.4 +…+ n.(n+1) =
1. [n(n+1)(2n+1)]/2
2. [n(n+1)(n+2)]/3
3. [n(n+1)/2]²
4. (3ⁿ-1)/2
For all n ∈ N ,1.2 + 2.2² + 3.2³ + ...+n.2ⁿ =
1. [n(n+1)(2n+1)]/2
2. n/(n+1)
3. (n–1) 2ⁿ⁺¹ + 2.
4. (3ⁿ-1)/2
For all n ∈ N ,a + ar + ar²+…+ arⁿ⁻¹ =
1. [r(r+1)(2a+1)]/2
2. a(rⁿ−1)/(r−1)
3. [a(r+1)/2]²
4. (3ⁿ-1)/2
2.7ⁿ + 3.5ⁿ⁻⁵ is divisible by ____, for all n ∈ N
1. 20
2. 22
3. 24
4. 26
10²ⁿ⁻¹ + 1 is divisible by .
1. 10
2. 11
3. 12
4. 13
For every natural number n, n(n²−1)is divisible by
1. 5
2. 4
3. 6
4. 2
P(n):2.7ⁿ+3.5ⁿ−5, ∀n∈N is divisible by
1. 24
2. 20
3. 10
4. 5