Question

tinh nhanh A = 1x2 + 2x3 + 3x4 + 4x5 +.............+ 99x100

Answer 1

A = 1x2 + 2x3 + ... + 99x100

3A = 1x2x3 + 2x3x(4-1) + ... + 99x100x(101-98)

3A = 1x2x3 + 2x3x4 - 1x2x3 + ... + 99x100x101 - 98x99x100

3A = 99x100x101

3A = 999900

A = 333300

Answer 2

Ta có:

A=1x2+2x3+3x4+4x5+...+99x100

3A=1x2x3+2x3x3+3x4x3+4x5x3+...+99x100x3

3A=1x2x3+2x3x(4-1)+3x4x(5-2)+4x5x(6-3)+...+99x100x(101-98)

3A=1x2x3+2x3x4-1x2x3+3x4x5-2x3x4+4x5x6-3x4x5+...+99x100x101-98x99x100

Suy ra 3A=99x100x101

A=99x100x101/3

A=333300

Answer 3

A = 1 . 2 + 2 . 3 + 3 . 4 + 4 . 5 +.............+ 99 . 100

A = 1 . 2 + 2 .3 + 3 . 4 + 4 . 5 + ...+ 99 . 100

A .  3 = 1 . 2 . 3 + 2 . 3 . 3 + 3 . 4 . 3 + 4. 5 . 3 + ... + 99 . 100 . 3

A . 3 = 1. 2 . 3 + 2 . 3 . (4-1) + 3 .4 . (5 - 2 ) + 4. 5 . (6- 3 )+... + 99 . 100. (101 -98 ) 

A . 3 = 1 . 2 . 3 + 2 . 3 . 4 - 1. 2 . 3 + 3 . 4 . 5 - 2 . 3 . 4 + 4 .5 . 6 - 3 . 4 . 5 + ... + 99 . 100 . 101 - 98 . 99.100.

A .  3 = 99 . 100 . 101

A = 99 . 100 . 101 : 3

A = 333 300