2+6+12+20+30= 70

Gọi biểu thức trên là A, ta có :

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

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

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

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

A x 3 = 99x100x101

A = 99x100x101 : 3

A = 333300

sai thì thui nhá,mk hok ngu lắm

ahihi

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

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

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

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

A x 3 = 99x100x101

A = 99x100x101 : 3

A = 333300

hok tốt

S= 1x2+2x3+3x4+4x5+...+ 20x21

3xS=3x( 1x2+2x3+3x4+4x5+...+ 20x21 )

3xS = 1x2x3+2x3x3+3x4x3+....+20x21x3

3xS = 1x2x3 + 2x3x(4-1) + 3x4x(5-2)+........+20x21x(22-19)

3xS= 1x2x3 + 2x3x4 - 1x2x3 + 3x4x5 - 2x3x4 +......+20x21x22 - 19x20x21

3xS = 20x21x22

 S = 20x21x22 /3

S= 1x2+2x3+3x4+4x5+...+ 20x21

3xS=3x( 1x2+2x3+3x4+4x5+...+ 20x21 )

3xS = 1x2x3+2x3x3+3x4x3+....+20x21x3

3xS = 1x2x3 + 2x3x(4-1) + 3x4x(5-2)+........+20x21x(22-19)

3xS= 1x2x3 + 2x3x4 - 1x2x3 + 3x4x5 - 2x3x4 +......+20x21x22 - 19x20x21

3xS = 20x21x22

S = 20x21x22 /3

k mk nha

Gọi biểu thức trên là A, ta có :

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

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

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

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

A x 3 = 99x100x101

A = 99x100x101 : 3

A = 333300

Gọi biểu thức trên là S, ta có :

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

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

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

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

S x 3 = 99x100x101

S = 99x100x101 : 3

S = 333300

=333300

k nha nha nha nha

mik k lại cho
 

1999x2000x2001:3=2666666000

Ta có :

\(S=\dfrac{1}{1.2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+\dfrac{1}{4.5}+..............+\dfrac{1}{99.100}\)

\(S=1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{5}+...........+\dfrac{1}{99}-\dfrac{1}{100}\)

\(S=1-\dfrac{1}{100}=\dfrac{99}{100}\)

\(\frac{1}{1x2}+\frac{1}{2x3}+...+\frac{1}{99x100}\)

=\(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{99}-\frac{1}{100}\)

=\(1-\frac{1}{100}\)

=\(\frac{99}{100}\)