Question

1.Tính nhanh

A=\(\dfrac{2}{7}\)+\(\dfrac{-3}{8}\)+\(\dfrac{11}{7}\)+\(\dfrac{1}{3}\)+\(\dfrac{1}{7}\)+\(\dfrac{5}{-3}\)

B=\(\dfrac{3}{17}\)+\(\dfrac{-5}{13}\)+\(\dfrac{-18}{35}\)+\(\dfrac{14}{17}\)+\(\dfrac{17}{-35}\)+\(\dfrac{-8}{13}\)

C=\(\dfrac{-3}{17}\)+(\(\dfrac{2}{3}\)+\(\dfrac{3}{17}\))

D=(\(\dfrac{-1}{6}\)+\(\dfrac{5}{-12}\))+\(\dfrac{7}{12}\)

2.a) Chứng tỏ:\(\dfrac{1}{201}\)+\(\dfrac{1}{212}\)+. . .+\(\dfrac{1}{399}\)+\(\dfrac{1}{400}\)

b)1 < \(\dfrac{1}{5}\)+\(\dfrac{1}{6}\)+. . .+\(\dfrac{1}{16}\)+\(\dfrac{1}{17}\)< 2

Answer 1

A=\(\dfrac{2}{7}+\dfrac{-3}{8}+\dfrac{11}{7}+\dfrac{1}{3}+\dfrac{1}{7}+\dfrac{5}{-3}\)

A=\(\left(\dfrac{2}{7}+\dfrac{11}{7}+\dfrac{1}{7}\right)+\left(\dfrac{1}{3}+\dfrac{5}{-3}\right)+\dfrac{-3}{8}\)

A=\(2+\dfrac{-4}{3}+\dfrac{-3}{8}\)

A=\(\dfrac{7}{24}\)

B=\(\dfrac{3}{17}+\dfrac{-5}{13}+\dfrac{-18}{35}+\dfrac{14}{17}+\dfrac{17}{-35}+\dfrac{-8}{13}\)

B=\(\left(\dfrac{3}{17}+\dfrac{14}{17}\right)+\left(\dfrac{-18}{35}+\dfrac{17}{-35}\right)+\left(\dfrac{-5}{13}+\dfrac{-8}{13}\right)\)

B=\(\dfrac{17}{17}+\dfrac{-35}{35}+\dfrac{-13}{13}\)

B=\(1+\left(-1\right)+\left(-1\right)=-1\)

C=\(\dfrac{-3}{17}+\left(\dfrac{2}{3}+\dfrac{3}{17}\right)\)

C=\(\dfrac{-3}{17}+\dfrac{2}{3}+\dfrac{3}{17}=\left(\dfrac{-3}{17}+\dfrac{3}{17}\right)+\dfrac{2}{3}\)

C=0+\(\dfrac{2}{3}=\dfrac{2}{3}\)

D=\(\left(\dfrac{-1}{6}+\dfrac{5}{-12}\right)+\dfrac{7}{12}\)

D=\(\dfrac{-1}{6}+\dfrac{5}{-12}+\dfrac{7}{12}\)

D=\(\dfrac{-2}{12}+\dfrac{-5}{12}+\dfrac{7}{12}=\left(\dfrac{-2}{12}+\dfrac{-5}{12}\right)+\dfrac{7}{12}\)

D=\(\dfrac{-7}{12}+\dfrac{7}{12}=0\)