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100^2 - 99^2 + 98^2 - 97^2 + 96^2 - 95^2 + ... + 2^2 - 1^2 = ?

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posted Jul 9, 2014 by Udita

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1 Solution

+1 vote

By this Formula (a+1)^2 - a^2 = 2a + 1 = (a+1) + a

so
100^2-99^2 = 100+ 99
98^2 - 97 ^2 = 98+97
96^2-95^2 = 96 + 95

so on
adding we get 100^2-99^2+98^2-97^2+...+2^2-1^2 =100 + 99 + 98 ... + 1 = sum of integers from 1 to 100 = 100 *101/2 = 5050

solution Jul 9, 2014 by Rahul Singh



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0 votes

Which set of numbers would most logically fill in the blanks in the following series?
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(a) 101 98
(b) 104 96
(c) 106 99
(d) none of these

Please provide your reasoning also?

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If
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