Question

[Nguyễn Thị Hiền Nga]

Tính bằng cách hợp lí :

a , \(\dfrac{1}{15}+\dfrac{9}{10}+\dfrac{14}{15}-\dfrac{11}{9}-\dfrac{20}{10}+\dfrac{1}{157}\)

b , \(\dfrac{1}{5}-\dfrac{-1}{3}+\dfrac{-1}{5}-\dfrac{2}{6}\)

c , \(\dfrac{2}{1\times3}+\dfrac{2}{3\times5}+...+\dfrac{2}{2015\times2017}\)

d , \(\dfrac{5}{1\times3}+\dfrac{5}{3\times5}+...+\dfrac{5}{2015\times2017}\)

e , \(\dfrac{1}{1\times2}+\dfrac{1}{3\times4}+...+\dfrac{1}{2016\times2017}\)

Answer 1

[Nguyễn Lê Phước Thịnh]

a: \(=\left(\dfrac{1}{15}+\dfrac{14}{15}\right)+\left(\dfrac{9}{10}-2-\dfrac{11}{9}\right)+\dfrac{1}{157}\)

\(=1+\dfrac{1}{157}+\dfrac{81-180-110}{90}\)

\(=\dfrac{158}{157}+\dfrac{-209}{90}\simeq-1.315\)

b: \(=\dfrac{1}{5}+\dfrac{1}{3}-\dfrac{1}{5}-\dfrac{2}{6}\)

=1/3-1/3

=0

c: \(\dfrac{2}{1\cdot3}+\dfrac{2}{3\cdot5}+...+\dfrac{2}{2015\cdot2017}\)

\(=1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+...+\dfrac{1}{2015}-\dfrac{1}{2017}\)

=2016/2017