Question: Sum of the series S= 12 – 22 + 32 – 42 +……–20022</s...

Question

Sum of the series S= 1² – 2² + 3² – 4² +……–2002² + 2003² is:

Answer 1

We can write S as

S = (1 – 2)(1 + 2) + (3 – 4)(3 + 4)……

(2001 – 2002) (2001 + 2002) + 2003²

̃ S = (–1)(1 + 2) + (–1)(3 + 4) …..(–1)

(2001 + 2002) + 2003²

S = (–1)[1 + 2 + 3 + 4 + 5 +…..2002]+ 2003²

= (-1) $\frac { ( 2002 \times 2003 ) } { 2 }$ + (2003)²

= – (1001×2003) + (2003)²

= (2003)(2003 – 1001)

= 2003 × (1002)

= 2007006

Question: Sum of the series S= 1<sup>2</sup> – 2<sup>2</sup> + 3<sup>2</sup> – 4<sup>2</sup> +……–2002<sup>2</s...