Question

[võ thị hồng thư]

Tính tổng :T=1^2_2²+3^2_4²+......+2015^2_2016²+2017²

Answer 1

[kaitovskudo]

Đặt A=1²-2²+.....-2016²

=> -A=2²-1²+4²-3²+6²-5²...+2016²-2015²

-A=(2-1)(2+1)+(4-3)(4+3)+(6-5)(6+5)...+(2016-2015)(2016+2015)

-A=3+7+11+...+4031

-A=[(4031-3):4+1]:2 x (3+4031)

-A=2033136

A=-2033136

Answer 2

[Huỳnh Thị Thùy Vy]

Đặt A=1²-2²+.....-2016²

=> -A=2²-1²+4²-3²+6²-5²...+2016²-2015²

-A=(2-1)(2+1)+(4-3)(4+3)+(6-5)(6+5)...+(2016-2015)(2016+2015)

-A=3+7+11+...+4031

-A=[(4031-3):4+1]:2 x (3+4031)

-A=2033136

A=-2033136