Question

[Nguyễn Thị Thu Phương]

Tính tổng T = 500^2 - 499^2 + 498^2 - 497^2 + ... + 2^2 - 1^2

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Answer 1

[Nguyễn Linh Chi]

T = 500^2 - 499^2 + 498^2 - 497^2 +...+2^2 -1^2

= 2( 500^2 + 498^2 + 496^2 +...+2^2 ) - ( 1^2 + 2^2 +3^2 + 4^2 +...+498^2 + 499^2) 

= 2.4 ( 1^2 + 2^2 + 3^2 + ...+249^2 + 250^2) - ( 1^2 + 2^2 +3^2 + 4^2 +...+498^2 + 499^2) 

\(=8.\frac{250\left(250+1\right)\left(2.250+1\right)}{6}-\frac{500\left(500+1\right)\left(2.500+1\right)}{6}\)

\(=\frac{500\left(500+1\right)}{6}\left(4.\left(250+1\right)-\left(2.500+1\right)\right)\)

= 250 ( 500 + 1)= 125250