-
1² – 2² + 3² – 4² + .... – 10² is equal to
-
- 45
- –45
- –54
- –55
- 45
Correct Option: D
Suppose S = 1² – 2² + 3² – 4² + ... – 10²
S = (1² + 3² + 5² + 7² + 9²) – (2² + 4² + 6² + 8² + 10²)
We know that ,
| Sum of squares of first n odd natural numbers = | |
| 3 |
| Sum of squares of first n even natural numbers = | n(n + 1)(2n + 1) | |
| 3 |
| Hence, S = | - | × 5(5 + 1) (2 × 5 + 1) | ||
| 3 | 3 |
| S = | = | ||
| 3 | 3 |
Therefore , S = 165 – 220 = – 55
