Hỏi đáp về Cộng, trừ số hữu tỉ - Đại số 7

Cho x, y, z, t \(\in\) N*

Chứng minh rằng:

\(M=\dfrac{x}{x+y+z}+\dfrac{y}{x+y+t}+\dfrac{z}{y+z+t}+\dfrac{t}{x+z+t}\) có giá trị không phải là số tự nhiên

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

8) \(A=\dfrac{9}{10}-\dfrac{1}{90}-\dfrac{1}{72}-\dfrac{1}{56}-\dfrac{1}{42}-\dfrac{1}{30}-\dfrac{1}{20}-\dfrac{1}{12}-\dfrac{1}{6}-\dfrac{1}{2}\)

9) \(B=\dfrac{1}{3}+\dfrac{1}{3^2}+\dfrac{1}{3^4}+...+\dfrac{1}{3^{2014}}+\dfrac{1}{3^{2015}}\)

10) \(P=\dfrac{\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{4}+...+\dfrac{1}{2005}}{\dfrac{2004}{1}+\dfrac{2003}{2}+\dfrac{2002}{3}+...+\dfrac{1}{2004}}\)

Tính : \(S_n=\dfrac{1}{1.2.3}+\dfrac{1}{2.3.4}+...+\dfrac{1}{n\left(n+1\right)\left(n+2\right)}\)

Tìm x, biết

\(\dfrac{x+2015}{5}+\dfrac{x+2016}{4}=\dfrac{x+2017}{3}+\dfrac{x+2018}{2}\)

tim x

2 - /3/2x - /1/4/=/-5/4

-1-1/2-1/4-1/8-...-1/1024

Tìm x, biết
a. x + \(\dfrac{3}{10}=\dfrac{-2}{15}\)
b. \(\dfrac{-11}{12}x+0,25=\dfrac{5}{6}\)
c. x + (x+1)+(x+2)+........................+(x+2002)=2004

Thực hiện phép tính
a. \(\dfrac{-1}{24}-\left\{\dfrac{1}{4}-\left(\dfrac{1}{2}-\dfrac{7}{8}\right)\right\}\)
b.\(\left(8\dfrac{5}{11}+3\dfrac{5}{8}\right)-3\dfrac{5}{11}\)

c.\(\dfrac{4}{9}:\left(\dfrac{-1}{7}\right)+6\dfrac{5}{9}:\left(\dfrac{-1}{7}\right)\)

d. \(\left(\dfrac{-1}{5}+\dfrac{3}{7}\right):\dfrac{2}{11}+\left(\dfrac{-4}{5}+\dfrac{4}{7}\right):\dfrac{2}{11}\)
M.n giúp mk nha

\(1,2-\dfrac{5}{6}x=\dfrac{2}{3}\)

1/1.2.3+1/2.3.4+1/3.4.5+.....+1/37.38.39

\(\dfrac{x+1}{10}+\dfrac{x+1}{11}+\dfrac{x+1}{12}+\dfrac{x+1}{13}=\dfrac{x+1}{14}+\dfrac{x+1}{15}\)

Tính :

a) 1+2+3+...+9999

b) 1+5+9+...1001

c) 1/2 . 2/3 . 3/4 . ... . 99/100

0,75-0,6+3/7+3/13/-2,75-2,2+11/7+11/13

Cho S = \(\dfrac{3}{4}+\dfrac{8}{9}+\dfrac{15}{16}+...+\dfrac{2499}{2500}\)

Chứng minh: S \(\notin\) N

\(\dfrac{x}{21}=\dfrac{2}{7}-\dfrac{4}{3}\)

Cho \(B=\dfrac{1}{5^2}+\dfrac{1}{6^2}+.......+\dfrac{1}{100^2}\)

C/m: \(\dfrac{1}{6}< B< \dfrac{1}{4}\)

Cho \(A=1+\dfrac{1}{3}+\dfrac{1}{5}+.......+\dfrac{1}{99}\)

\(B=\dfrac{1}{1.99}+\dfrac{1}{3.97}+.......+\dfrac{1}{97.3}+\dfrac{1}{99.1}\)

Tính A : B

1

a) \(\left(x-1\right)^5=-243\)

b)\(\dfrac{x+2}{11}+\dfrac{2+x}{12}+\dfrac{x+2}{13}=\dfrac{+2x}{14}+\dfrac{x+2}{15}\)

c)x-2\(\sqrt{x}\)=0

1/99 - 1/99.98 - 1/98.97 - 1/97.96 -...-1/3.2 -1/2.1

Tìm x:

\(\dfrac{x-1}{59}+\dfrac{x-2}{58}+\dfrac{x-3}{57}=\dfrac{x-4}{56}+\dfrac{x-5}{55}+\dfrac{x-6}{54}\)

Tìm GTNN

\(\left(x+1\right)^2+\left(x+2\right)^2+\left(x+3\right)^2+\left(x+4\right)^2\)

tìm x biết :

( 5.x - 1 ) . ( 2. x -\(\dfrac{1}{3}\)) = 0

các bn ơi giúp mk vs nha mai mk nộp bài r

Chung minh rang tong sau khong la so tu nhien :

A = \(\dfrac{1}{2^2}\) + \(\dfrac{1}{3^2}\) + \(\dfrac{1}{4^2}\) + ..........+ \(\dfrac{1}{100^2}\)