1. The sum of the series 1³ + 2³ + 3³ + ………..n³ is

2. If n is an odd positive integer, then an + bn is divisible by :

3. 1/(1 ∙ 2) + 1/(2 ∙ 3) + 1/(3 ∙ 4) + ….. + 1/{n(n + 1)}

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

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

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

7. 1/(1 ∙ 2 ∙ 3) + 1/(2 ∙ 3 ∙ 4) + …….. + 1/{n(n + 1)(n + 2)} =

8. The nth terms of the series 3 + 7 + 13 + 21 +………. is

9. n(n + 1)(n + 5) is a multiple of ____ for all n ∈ N

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