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Question: The sum of n terms of the series 1<sup>2</sup> – 2<sup>2</sup> + 3<sup>2</sup> – 4<sup>2</sup> + 5<...

The sum of n terms of the series

12 – 22 + 32 – 42 + 52 – 62+ ..... is –

A
B

n(n + 1)

C

−n(n+1)2\frac { - \mathrm { n } ( \mathrm { n } + 1 ) } { 2 }

D

– n(n + 1)

Answer

−n(n+1)2\frac { - \mathrm { n } ( \mathrm { n } + 1 ) } { 2 }

Explanation

Solution

(1–2)(1+2) + (3 – 4)(3 + 4) + (5 – 6)(5+ 6) + .......

= – (1 + 2 + 3 + 4 + ....... n terms) = – n(n+1)2\frac { \mathrm { n } ( \mathrm { n } + 1 ) } { 2 }