Cho phân số \(\dfrac{x}{3}\)Điền vào chỗ trống

Nếu \(\dfrac{x}{3}\)< 0 thì x=.

Nếu 0 < \(\dfrac{x}{3}\) < 1 thì x --..

Nếu \(\dfrac{x}{3}\)= 0 thì x --

tìm x,y ∈ N biết 5x14y chia hết cho 2,5,9

chứng minh rằng với mọi số tự nhiên n khác 0 ta đều có:

a) \(\dfrac{1}{2.5}+\dfrac{1}{5.8}+\dfrac{1}{8.11}+-+\dfrac{1}{\left(3n-1\right)\left(3n+2\right)}=\dfrac{n}{6n+4}\)

tìm x:

\(\left(1-\dfrac{1}{2}\right)\cdot\left(1-\dfrac{1}{3}\right)\cdot\left(1-\dfrac{1}{4}\right)\cdot...\cdot\left(1-\dfrac{1}{10}\right)=\dfrac{x}{2010}\)

Tìm x;

a,\(\left(1-\dfrac{1}{3}\right)\)*\(\left(1-\dfrac{1}{6}\right)\)*\(\left(1-\dfrac{1}{10}\right)\)*...*\(\left(1-\dfrac{1}{780}\right)\)*x=1

C=\(\dfrac{2}{15}+\dfrac{2}{35}+\dfrac{2}{63}+...+\dfrac{2}{399}\)

E=\(\dfrac{6}{1.3.7}+\dfrac{6}{6.7.9}+...+\dfrac{6}{13.15.19}\)

F=\(\dfrac{92-\dfrac{1}{9}-\dfrac{2}{10}-\dfrac{3}{11}-...-\dfrac{92}{100}}{\dfrac{1}{9}+\dfrac{1}{10}+...+\dfrac{1}{100}}\)

G=\(10-\dfrac{1}{72}-\dfrac{1}{56}-\dfrac{1}{42}-...-\dfrac{1}{6}-\dfrac{1}{2}\)

Tính một cách hợp lý:

a\(\left(\dfrac{1}{2}-1\right)\left(\dfrac{1}{3}-1\right)...\left(\dfrac{1}{100}-1\right)\)) \(x:\dfrac{99}{100}:\dfrac{98}{99}:...:\dfrac{2}{3}:\dfrac{1}{2}\)

b) \(\dfrac{5-\dfrac{5}{3}+\dfrac{5}{9}-\dfrac{5}{27}}{8-\dfrac{8}{3}+\dfrac{8}{9}-\dfrac{8}{27}}:\dfrac{15-\dfrac{15}{11}+\dfrac{15}{121}}{16-\dfrac{16}{11}+\dfrac{16}{121}}\)

c) \(\dfrac{\dfrac{1}{9}-\dfrac{5}{6}-4}{\dfrac{7}{12}-\dfrac{1}{36}-10}\)

d) \(\left(\dfrac{1}{2}+1\right)\left(\dfrac{1}{3}+1\right)...\left(\dfrac{1}{99}+1\right)\)

e)

-15/12 . x+ 3/7=6/5 .x -1/2

CMR:1×3×5×7×...×19=11/2×12/2×13/2×...×20/2

Cho 3 số nguyên a, b, c. Chứng minh rằng:

a) Nếu a = b + c thì a/b + a/c = a/b x a/c

b) Nếu c = a + b thì a/b - a/c = a/b x a/c