Hỏi đáp về Phép cộng phân số - Số học 6

giúp mk vs

a) \(2x-\dfrac{1}{4}=\dfrac{1}{2}\)

b) \(\dfrac{-2}{3}.x+\dfrac{1}{5}=\dfrac{3}{10}\)

Tính giá trị của biểu thức :\(\left(\dfrac{1}{200}+\dfrac{1}{300}+\dfrac{1}{400}+...+\dfrac{1}{1000}\right).1.2.3.4.5.\left(\dfrac{1}{120}-\dfrac{1}{180}-\dfrac{1}{360}\right)\)

Cụ thể nhế

1. 0.1+0.2-0.3-04+0.5+0.6-0.7-0.8+0.9

2. 2/1x4 + 2/4x7 + ... + 2/94x97 + 2/97x100

Chứng minh 1/3^2+1/4^2+1/100^2 < 1/2

Cho \(A=\dfrac{1}{3^2}+\dfrac{1}{6^2}+\dfrac{1}{9^2}+...+\dfrac{1}{9n^2}.\)

Chứng tỏ rằng

A\(< \dfrac{2}{9}\)

Thực hiện phép tính:

1/10+1/40+1/88+1/154+1/238

Giúp mình với nha ^_^

1.Tìm x, y thuộc Z :

50- 5*(x + 3 )³=2|3- y|

2.Tính :

a, \(\dfrac{-1}{20}+\dfrac{-1}{30}+\dfrac{-1}{42}+\dfrac{-1}{56}+\dfrac{-1}{72}+\dfrac{-1}{90}\)

b,\(\dfrac{5}{2.1}+\dfrac{4}{1.11}+\dfrac{3}{11.2}+\dfrac{1}{2.15}+\dfrac{13}{15.4}\)

3.Tìm x :

a, \(\dfrac{x-5}{8}=\dfrac{18}{x-5}\) b, ( x-2 )¹⁰= ( 2-x )⁸

Tính \(A=\dfrac{4}{5.7}+\dfrac{4}{7.9}+............+\dfrac{4}{59.61}\)

P=\(\dfrac{1}{1\cdot2}\)+\(\dfrac{2}{2\cdot4}\)+\(\dfrac{3}{4\cdot7}\)+...+\(\dfrac{10}{46\cdot56}\)

Tính nhanh 1/2+1/14+1/35+1/65+1/104+1/152

Chứng minh 4^2/20.24+4^2/24.28+...+4^2/76.80 < 1

chung minh rang 1+\(\frac{1}{2}\)+\(\frac{1}{3}\)+\(\frac{1}{4}\)+...+\(\frac{1}{31}\)<5

tính

\(\dfrac{3}{5.7}+\dfrac{3}{7.9}+\dfrac{3}{9.11}+...+\dfrac{3}{59.61}\)

Tính :

A=\(\dfrac{1}{10}+\dfrac{1}{15}+\dfrac{1}{21}+......+\dfrac{1}{120}\)

B=\(\dfrac{4}{3.7}+\dfrac{4}{7.11}+\dfrac{4}{11.15}+......+\dfrac{4}{107.111}\)

C=\(\dfrac{7}{10.11}+\dfrac{7}{11.12}+\dfrac{7}{12.13}+......+\dfrac{7}{69.70}\)

D=\(\dfrac{15}{90.94}+\dfrac{15}{94.98}+\dfrac{15}{98.102}+......+\dfrac{15}{146.150}\)

Tính giá trị của A=1/30+1/42+1/56+1/72+1/90+1/110+1/132

chứng tỏ

\(\dfrac{1}{5}\)+\(\dfrac{1}{6}\)+\(\dfrac{1}{7}\)+.....+\(\dfrac{1}{17}\)<2

Chứng minh rằng :

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

Tính

A=\(\dfrac{\dfrac{2017}{2}+\dfrac{2017}{3}+\dfrac{2017}{4}+...+\dfrac{2017}{2018}}{\dfrac{2017}{1}+\dfrac{2016}{2}+...+\dfrac{1}{2017}}\)

Cho biểu thức D= \(\dfrac{1}{3}+\dfrac{1}{3^2}+\dfrac{1}{3^3}+...+\dfrac{1}{3^{100}}\). Chứng minh rằng D<\(\dfrac{1}{2}\)

Tìm x biết

Cho A=\(\dfrac{1}{3}+\dfrac{1}{6}+\dfrac{1}{10}+.....+\dfrac{1}{x.\left(x+1\right)}\)\(=\dfrac{2014}{2016}\)

CMR:

a) \(\dfrac{1}{2^2}+\dfrac{1}{4^2}+\dfrac{1}{6^2}+...+\dfrac{1}{100^2}< \dfrac{1}{2}\)

b) \(\dfrac{3}{4}+\dfrac{8}{9}+\dfrac{15}{16}+...+\dfrac{2499}{2500}>48\)

Tính nhanh:

a) \(A=\dfrac{5}{1\cdot5}=\dfrac{5}{5\cdot10}+\dfrac{5}{10\cdot15}+...+\dfrac{5}{9995\cdot10000}\)

b) \(B=\dfrac{1}{420}+\dfrac{1}{462}+\dfrac{1}{506}+...+\dfrac{1}{1560}\)

Cho A=1/1²+1/2²+1/2²+1/3²+1/4²+..........+ 1/50²<2

Tìm x\(\in\) Z, biết: \(\dfrac{1}{3}+\dfrac{1}{6}+\dfrac{1}{10}+...+\dfrac{2}{x.\left(x+1\right)}\) =\(\dfrac{2014}{2016}\)

Cc bn ơi giúp mk vs mk đg rất gấp!!!!!!!