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Solve 100^2 - 99^2 - 97^2 + 96^2 - 95^2 + .. + 2^2 - 1^2 = ?
Solve 100^2 - 99^2 - 97^2 + 96^2 - 95^2 + .. + 2^2 - 1^2 = ?
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Answer:: 5050
Explanation::You must have noticed that 50 pairs of n^2 – (n-1) ^2 exist.
n^2 – (n-1)^2 = n + (n – 1)
In such case, we may as well write 100^2 - 99^2 + 98^2 - 97^2 + 96^2 - 95^2 + ... + 2^2 - 1^2 as 100 + 99 + 98+ ... + 2 + 1 = (100 x 101)/2 = 5050
Explanation::You must have noticed that 50 pairs of n^2 – (n-1) ^2 exist.
n^2 – (n-1)^2 = n + (n – 1)
In such case, we may as well write 100^2 - 99^2 + 98^2 - 97^2 + 96^2 - 95^2 + ... + 2^2 - 1^2 as 100 + 99 + 98+ ... + 2 + 1 = (100 x 101)/2 = 5050
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