Gọi tổng đã cho là A.

Ta có: A = 1/1x2x3 + 1/2x3x4 + 1/3x4x5 +1/4x5x6 .... + 1/10x11x12 Chú ý rằng: 1/1x2x3 = 1/2 x(1/1x2 - 1/2x3) 1/2x3x4 =1/2 x (1/2x3 - 1/3x4) 1/3x4x5 = 1/2 x (1/3x4 - 1/4x5) ..........

Từ đó suy ra: A = 1/2 x (1/1x2 - 1/2x3 + 1/2x3 - 1/3x4+1/3x4 - 1/4x5+...+ 1/10x11 - 1/11x12) = 1/2 x (1/1x2 - 1/11x12) =1/2 x ( 1/2 - 1/132) = 65/264

Đặt tổng trên = A

Có : A = 1/1.2.3 + 1/2.3.4 + ...... + 1/9.10.11

2A = 2/1.2.3 + 2/2.3.4 + ...... + 2/9.10.11

     = 1/1.2 - 1/2.3 + 1/2.3 - 1/3.4 + ....... + 1/9.10 - 1/10.11

     = 1/1.2 - 1/10.11

     = 1/2 - 1/110 = 27/55

=> A = 27/55 : 2 = 27/110

Tk mk nha

Ta có:

\(A=\frac{6}{15.18}+\frac{6}{18.21}+\frac{6}{21.24}+...+\frac{6}{87.90}\)

\(A=2.\left(\frac{3}{15.18}+\frac{3}{18.21}+\frac{3}{21.24}+...+\frac{3}{87.90}\right)\)

\(A=2.\left(\frac{1}{15}-\frac{1}{18}+\frac{1}{18}-\frac{1}{21}+\frac{1}{21}-\frac{1}{24}+...+\frac{1}{87}-\frac{1}{90}\right)\)

\(A=2.\left(\frac{1}{15}-\frac{1}{90}\right)\)

\(A=2.\frac{1}{18}=\frac{1}{9}\)

a) = (-24 + 24) + 6+  10 = 16 

b) = (23 - 23) + (15 - 25) = -10

c) = (-350  + 350) + (-3 -7) = -10

d) = (-9 - 11 - 1) + 21 = -21 + 21 = 0 

a) (-24) + 6 + 10 + 24

= (-24) + 24 + 6 + 10

= 0 + 6 + 10

= 16

b) 15 + 23 + (-25) + ( -23)

= 23 + (-23) + 15 + (-25)

= 0 + 15 + (-25)

= 15 + (-25)

= -10

c) (-3) + (-350) + (-7) + 350

= (-350) + 350 + (-3) + (-7)

= 0 +(-3) + (-7)

= -10

d) (-9) + (-11) + 21 + (-1)

= - 20 + [ 21 + (-1) ]

= -20 + 20

= 0 

T = \(\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+\frac{1}{5\cdot6}+...+\frac{1}{98\cdot99}+\frac{1}{99\cdot100}=\)

T = \(\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{98}-\frac{1}{99}+\frac{1}{99}-\frac{1}{100}=\)

T = \(\frac{1}{1}-\frac{1}{100}=\)

T = \(\frac{99}{100}\)