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Summation by Sigma Method

The series ...

Question

The series $1^{2} - 2^{2} + 3^{2} - 4^{2} + . . . . . + 99^{2} - 100^{2} =$ _____

A

- 5050

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B

5050

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C

11000

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D

- 11000

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Solution

The correct option is C $- 5050$
The sum of nth term of the series is given as
$S = (- 1)^{n + 1} \frac{n (n + 1)}{2}$
Here $n = 100$
So,
$S = (- 1)^{100 + 1} \frac{100 (100 + 1)}{2}$
$= (- 1) \frac{10100}{2}$
$= - 5050$

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