Question

1^2-2^2 + 3^2-4^2 + 5^2-6^2 + . . . . . + 99^2 - 100^ 2​

Answer 1

Answer:

- 5050

Step-by-step explanation:

⇒ 1² - 2² + 3² - 4² + 5² - 6² + ... 99² - 100²

⇒ (1² - 2²) + (3² - 4²) + (5² - 6²) + ... (99² - 100²)

   Using a² - b² = (a + b)(a - b)

⇒ (-1)(3) + (-1)(7) + (-1)(11) + ... (-1)(199)

⇒ - [3 + 7 + 11 + ... 199]

This forms an arithematic series in which a = 3 and d = 4, and n = 100/2 = 50.

∴ S = (n/2) [1st term + last term]

      = (50/2) [3 + 199]

      = 5050

Hence,

Required sum is - [3 + 7 + 11 + ... 199]  = - 5050

Answer 2

Step-by-step explanation:

uttar uttar uttar = 5050