1. For any natural number n, 7ⁿ – 2ⁿ is divisible by

2. (n² + n) is ____ for all n ∈ N.

3. For all n ∈ N, 3×5²ⁿ⁺¹ + 2³ⁿ⁺¹ is divisible by

4. Find the number of shots arranged in a complete pyramid the base of which is an equilateral triangle, each side containing n shots.

5. {1 – (1/2)}{1 – (1/3)}{1 – (1/4)} ……. {1 – 1/(n + 1)} =

6. (1 + x)n ≥ ____ for all n ∈ N,where x > -1

7. 10^2n-1 + 1 is divisible by ____ for all N ∈ N

8. For all n∈N, 7²ⁿ − 48n−1 is divisible by :

9. The sum of the series 1² + 2² + 3² + ………..n² is

10. {1/(3 ∙ 5)} + {1/(5 ∙ 7)} + {1/(7 ∙ 9)} + ……. + 1/{(2n + 1)(2n + 3)} =