Oxford University MAT 2020 Solved Papers

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Question : 3 of 10

Marks: +1, -0

The sum

1-4+9-16+⋯+99^2-100^2

equals

-101
$-1000$
-1111
$-4545$
$-5050$ .

Solution:

Pair the terms to get

-3-7-⋯-199

. This is the sum of an arithmetic progression and is equal to

(-3-199) × 50 \/ 2=-5050

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