Question

100²-99²+98²-97²+96²-95²+..........+2²-1²

Nguyễn Thành Trương Lê Thanh Nhàn

Answer 1

Đặt A = 100 2 − 99 2 + 98 2 − 97 2 + 96 2 − 95 2 + ... + 2 2 − 1 2

A = (100 2 − 99 2 ) + (98 2 − 97 2 ) + ... + (2 − 1 2 2 ) A = 2.100 − 1 + 2.98 − 1 + 2.96 − 1 + ... + 2.2 − 1 A = 2.(100 + 98 + ... + 2) − 50 A = − 2 2. [(100 − 2) : 2 + 1] .(100 + 2) 50 Các A = 50.102 − 50 A = 50.(201 − 1) A = 50.101 A = 5050

Answer 2

100² - 99² + 98² - 97² + 96² - 95² +..........+ 2² - 1²

= ( 100² - 99² ) + ( 98² - 97² ) + ( 96² - 95² ) +....+ ( 2² - 1² )

= ( 100 - 99 ) ( 100 + 99 ) + (98 - 97)(98 + 97) + ....+ (2 - 1)(2 + 1)

= 199 + 195 + ....+3 ( có: \(\frac{199-3}{4}+1\) = 50 số hạng)

= \(\frac{\left(199+3\right).50}{2}\) = 5050