find 100²-99²+98²-97²+...+2²-1².
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Given:
100^2 - 99^2 + 98^2 - 97^2 +....+2^2 - 1^2
Rearranging the above equation,
= (100^2 - 1^2) - (99^2 - 2^2) + (98^2 - 3^2) -.......+ (52^2 - 49^2) - (51^2 - 50^2)
Using
(a^2 - b^2) = (a + b)(a - b), we get
= 101*99 - 101*97 + 101*95 - ....... + 101*3 - 101*1
= 101*(99 - 97 + 95 - 93 +...+ 3 - 1)
Subtracting every two terms in the above equation we get,
= 101*(2 + 2 + ........ 50 terms)
= 101*2*50
= 101*100
= 10100 ——> Answer
100^2 - 99^2 + 98^2 - 97^2 +....+2^2 - 1^2
Rearranging the above equation,
= (100^2 - 1^2) - (99^2 - 2^2) + (98^2 - 3^2) -.......+ (52^2 - 49^2) - (51^2 - 50^2)
Using
(a^2 - b^2) = (a + b)(a - b), we get
= 101*99 - 101*97 + 101*95 - ....... + 101*3 - 101*1
= 101*(99 - 97 + 95 - 93 +...+ 3 - 1)
Subtracting every two terms in the above equation we get,
= 101*(2 + 2 + ........ 50 terms)
= 101*2*50
= 101*100
= 10100 ——> Answer
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