\(A=\frac{2}{3}+\frac{14}{15}+\frac{34}{35}+\frac{62}{63}+\frac{98}{99}+\frac{142}{143}\)

\(=\left(1-\frac{1}{3}\right)+\left(1-\frac{1}{15}\right)+\left(1-\frac{1}{35}\right)+\left(1-\frac{1}{63}\right)+\left(1-\frac{1}{99}\right)+\left(1-\frac{1}{143}\right)\)

\(=\left(1+1+1+1+1+1\right)-\left(\frac{1}{3}+\frac{1}{15}+\frac{1}{35}+\frac{1}{63}+\frac{1}{99}+\frac{1}{143}\right)\)

\(=6-\left(\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+\frac{1}{9.11}+\frac{1}{11.13}\right)\)

\(=6-\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}+\frac{1}{11}-\frac{1}{13}\right)\)

\(=6-\left(1-\frac{1}{13}\right)\)

\(=6-1+\frac{1}{13}\)

\(=5+\frac{1}{13}\)

\(=\frac{66}{13}\)

Mk sửa lại 1 tí nha dòng thứ 5 :

\(A=6-\frac{1}{2}\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}+\frac{1}{11}-\frac{1}{13}\right)\)

\(=6-\frac{1}{2}\left(1-\frac{1}{13}\right)\)

\(=6-\frac{1}{2}.\frac{12}{13}\)

\(=6-\frac{6}{13}=\frac{72}{13}\)

Mong bn bỏ qua nha

\(5-\dfrac{2}{3}-\dfrac{14}{15}+\dfrac{1}{35}-\dfrac{62}{63}-\dfrac{98}{99}-\dfrac{142}{143}\)

\(=5-\left(1-\dfrac{1}{3}\right)-\left(1-\dfrac{1}{15}\right)+\dfrac{1}{35}-\left(1-\dfrac{1}{63}\right)-\left(1-\dfrac{1}{99}\right)-\left(1-\dfrac{1}{143}\right)\)

\(=5-1+\dfrac{1}{1\cdot3}-1+\dfrac{1}{3\cdot5}+\dfrac{1}{5\cdot7}-1+\dfrac{1}{7\cdot9}-1+\dfrac{1}{9\cdot11}-1+\dfrac{1}{11\cdot13}\)

\(=1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+...+\dfrac{1}{11}-\dfrac{1}{13}\)

\(=1-\dfrac{1}{13}=\dfrac{12}{13}\)

10296 nha bn

tử 1 đến 143 có 143 số hạng.

tổng dãy là:

(143 + 1) x 143 : 2 = 10 296

ĐS................................

=10296 nha người anh em

a) 48, 96, 192, 384, 768

b) 19, 25, 32, 40, 49

c) 36, 51, 68, 89, 113

a) -321  + (-29) - 142  - (-72)

= [-321  +(-29)]+ [(-142)  + 72]

= [-(321 + 29)] + [- (142 - 72)]

= (-350) + (-70)

= -(350 + 70)

= -420

b) 214 - (-36) + (-305)

= 214 + 36 - 305

= 250 - 305

= -(305 - 250)

= -55.

\(144-143+142-141+...+4-3+2-1\)

\(=1+1+..+1+1\)

=72

\(a,=a-b+c-d-a-b-c-d=-2b-2d\\ b,=-a+b-c+a-b-a+b-c=-a+b-2c\)

a) ( a - b + c -d ) - ( a+ b + c + d ) = a - b + c - d - a - b - c - d = -2b - 2d 

b) ( -a + b -c ) + ( a - b ) - ( a- b + c ) = -a + b - c + a - b - a + b - c = -a + b - c - c = -a + b - 2c 

c) - ( a - b - c ) + ( b - c + d ) - ( -a + b + d )

\(1,\\ a,=\left[x^3\left(x-2\right)-4x\left(x-2\right)\right]:\left(x^2-4\right)\\ =x\left(x^2-4\right)\left(x-2\right):\left(x^2-4\right)=x\left(x-2\right)\\ b,=\left(2014-14\right)^2=2000^2=4000000\\ 2,\\ A=2015\cdot2013\cdot\left(2014^2+1\right)\\ A=\left(2014^2-1\right)\left(2014^2+1\right)\\ A=2014^4-1< B=2014^4\)

\(\dfrac{a+2b-ab-2b^2}{1-b}=\dfrac{\left(a+2b\right)-b\left(a+2b\right)}{1-b}=\dfrac{\left(1-b\right)\left(a+2b\right)}{1-b}=a+2b\)