Question

find 100²-99²+98²-97²+...+2²-1².​

Answer 1

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