Question

Tính nhanh :

\(\dfrac{1}{10}\)+ \(\dfrac{-1}{11}\)+ \(\dfrac{1}{12}\)+ \(\dfrac{-1}{13}\)+ \(\dfrac{1}{14}\)+ \(\dfrac{-1}{15}\)+ \(\dfrac{1}{16}\)+ \(\dfrac{1}{15}\)+ \(\dfrac{-1}{14}\)+ \(\dfrac{1}{13}\)+ \(\dfrac{-1}{12}\)+ \(\dfrac{-1}{12}\)+ \(\dfrac{1}{11}\)+ \(\dfrac{-1}{10}\)

Answer 1

\(=\left(\dfrac{1}{10}+\dfrac{-1}{10}\right)+\left(-\dfrac{1}{11}+\dfrac{1}{11}\right)+\left(-\dfrac{1}{12}+\dfrac{1}{12}\right)+\left(-\dfrac{1}{13}+\dfrac{1}{13}\right)+\left(-\dfrac{1}{14}+\dfrac{1}{14}\right)+\left(-\dfrac{1}{15}+\dfrac{1}{15}\right)+\dfrac{1}{16}\\ =\dfrac{1}{16}\)

Answer 2

Tính nhanh :

\(\dfrac{1}{10}+\dfrac{-1}{11}+\dfrac{1}{12}+\dfrac{-1}{13}+\dfrac{1}{14}+\dfrac{-1}{15}+\dfrac{1}{16}+\dfrac{-1}{10}+\dfrac{1}{11}+\dfrac{-1}{12}+\dfrac{1}{13}+\dfrac{-1}{14}+\dfrac{1}{15}\)

\(=\left(\dfrac{1}{10}+\dfrac{-1}{10}\right)+\left(\dfrac{-1}{11}+\dfrac{1}{11}\right)+\left(\dfrac{1}{12}+\dfrac{-1}{12}\right)+\left(\dfrac{-1}{13}+\dfrac{1}{13}\right)+\left(\dfrac{1}{14}+\dfrac{-1}{14}\right)\)

\(+\left(\dfrac{-1}{15}+\dfrac{1}{15}\right)+\dfrac{1}{16}\)

\(=0+0+...+0+\dfrac{1}{16}\)

\(=\dfrac{1}{16}\)

Answer 3

\(\dfrac{1}{10}+\dfrac{-1}{10}+\dfrac{1}{12}+-\dfrac{1}{13}+\dfrac{1}{14}+\dfrac{-1}{15}+\dfrac{1}{16}+\dfrac{1}{15}+\dfrac{-1}{14}+\dfrac{1}{13}+\dfrac{-1}{12}+\dfrac{-1}{12}+\dfrac{1}{11}+\dfrac{-1}{10}\)

=\(\left(\dfrac{1}{10}+\dfrac{-1}{10}\right)+\left(\dfrac{-1}{11}+\dfrac{1}{11}\right)+\left(\dfrac{1}{12}+\dfrac{-1}{12}\right)+\left(\dfrac{-1}{13}+\dfrac{1}{13}\right)+\left(\dfrac{1}{14}+\dfrac{-1}{14}\right)+\left(\dfrac{-1}{15}+\dfrac{1}{15}\right)+\dfrac{1}{16}+\dfrac{-1}{12}\)

=\(\dfrac{1}{16}+\dfrac{-1}{12}\)

=\(\dfrac{-1}{48}.\)