Special Series – Σn, Σn², Σn³, Method of Differences

Grade 11 Maths Higher — Special Series – Σn, Σn², Σn³, Method of Differences: 25 practice questions with instant scoring and explanations.

1. ∑(r=1 to n) r =
2. ∑(r=1 to n) r² =
3. ∑(r=1 to n) r³ =
4. The sum 1 + 2 + 3 + ... + 100 equals:
5. ∑(r=1 to 10) r² =
6. ∑(r=1 to 5) r³ =
7. The sum 1² + 2² + 3² + ... + 20² equals:
8. ∑(r=1 to n) (2r - 1) =
9. The method of differences is used when:
10. For the series 1·2 + 2·3 + 3·4 + ... + n(n+1), the sum is:
11. ∑(r=1 to n) r(r+1) =
12. The sum ∑(r=1 to 8) r³ equals:
13. For the series 1/(1·2) + 1/(2·3) + 1/(3·4) + ... + 1/(n(n+1)), the sum is:
14. ∑(r=1 to n) (r² - r) =
15. The sum 1³ + 2³ + 3³ + ... + 10³ =
16. ∑(r=1 to n) (2r² - r) =
17. For the series 1·2·3 + 2·3·4 + ... + n(n+1)(n+2), the sum is:
18. ∑(r=1 to 6) r(r + 1) =
19. The sum of ∑(r=1 to n) 1/(r(r+1)(r+2)) is:
20. ∑(r=1 to n) (r³ - r) =
21. For finding ∑(r=1 to n) rⁿ using method of differences, we use:
22. The sum ∑(r=1 to n) r/(r+1)! =
23. ∑(r=1 to 12) r equals:
24. The sum ∑(r=1 to n) 1/(r² + r) using partial fractions is:
25. ∑(r=1 to n) r(r-1) =