\(Q\left(x\right)=\dfrac{1}{x\left(x+1\right)}+\dfrac{1}{\left(x+1\right)\left(x+2\right)}+...+\dfrac{1}{\left(x+99\right)\left(x+100\right)}\)

\(=\dfrac{1}{x}-\dfrac{1}{x+1}+\dfrac{1}{x+1}-\dfrac{1}{x+2}+...+\dfrac{1}{x+99}-\dfrac{1}{x+100}\)

\(=\dfrac{1}{x}-\dfrac{1}{x+100}\)

\(=\dfrac{x+100-x}{x\left(x+100\right)}\)

\(=\dfrac{100}{x\left(x+100\right)}\)

#\(Toru\)

Câu 2:

P = x + 2 - x - 8 2 = 10 2  = 100.

Biểu thức P có giá trị bằng 100 tại mọi giá trị của x.

\(199\cdot201=\left(200-1\right)\left(200+1\right)=200^2-1=40000-1=39999\)

97.13 + 130.0,3 = 97.13 + 13.10.0,3

= 97.13 + 13.3 = 13.(97 + 3) = 13.100=1300

86.153 − 530.8,6 = 86.153 – 53.10.8,6

= 86.153 − 53.86 = 86.(153 − 53) = 86.100=8600

16^2-116^2

=256-13456

=-13200

HK TỐT^^

123² - 123.46 + 23²

= 123² - 2.123.23 + 23²

= (123 - 23)²

= 100²

= 10000

\(A=\left(2012-1\right)\left(2012+1\right)-2012^2=2012^2-1-2012^2=-1\)

\(A=\left(2012-1\right)\left(2012+1\right)-2012^2=2012^2-1-2012^2=-1\)

1 , 6 2 + 4 . 0 , 8 . 3 , 4 + 3 , 4 2 = 1 , 6 2 + 2 . 1 , 6 . 3 , 4 + 3 , 4 2   v ì   4 . 0 , 8 = 2 . 2 . 0 , 8 = 2 . 1 , 6 = 1 , 6 + 3 , 4 2 = 5 2 = 25