CTET Paper I (Classes I to V) Feb 2015 Solved Paper

Concept:Group the terms in pairs to simplify the alternating sum.Explanation:Combine each odd negative term with the next even positive term: $(-1+2)$, $(-3+4)$, $(-5+6)$, …, up to $(-999+1000)$. Each pair equals $1$. There are $1000$ terms, so $500$ such pairs. Total sum = $1 + 1 + \dots$ (500 times) = $500$. Alternatively, rearrange as $-(1+3+5+\dots+999) + (2+4+6+\dots+1000)$. Both sequences are arithmetic progressions with $500$ terms each. Sum of odds: $\frac{500}{2}(1+999)=250\times1000=250000$. Sum of evens: $\frac{500}{2}(2+1000)=250\times1002=250500$. Total = $-250000+250500=500$. Answer:$500$ (Option D)