Question

Tính hợp lí:

\(1-\dfrac{1}{2}+2-\dfrac{2}{3}+3-\dfrac{3}{4}-4-\dfrac{1}{3}-2-\dfrac{1}{2}-1\)

Answer 1

= 3 - 4 - 1 - 1 - 3/4

= -15/4

Answer 2

\(1-\dfrac{1}{2}+2-\dfrac{2}{3}+3-\dfrac{3}{4}-4-\dfrac{1}{3}-2-\dfrac{1}{2}-1=\left(1-1\right)-\left(\dfrac{1}{2}+\dfrac{1}{2}\right)+\left(3-4\right)-\left(\dfrac{1}{3}+\dfrac{2}{3}\right)+\left(2-2\right)-\dfrac{3}{4}=0-1-1-1+0-\dfrac{3}{4}=-3-\dfrac{3}{4}=-\dfrac{15}{4}\)

Answer 3

\(1-\dfrac{1}{2}+2-\dfrac{2}{3}+3-\dfrac{3}{4}-4-\dfrac{1}{3}-2-\dfrac{1}{2}-1\)

\(=\left(1-1\right)+\left(2-2\right)+\left(3-4\right)+\left(-\dfrac{1}{2}-\dfrac{1}{2}\right)+\left(-\dfrac{2}{3}-\dfrac{1}{3}\right)-\dfrac{3}{4}\)

\(=0+0+\left(-1\right)+\left(-1\right)+\left(-1\right)-\dfrac{3}{4}\)

\(=-3-\dfrac{3}{4}\)

\(=\dfrac{-12}{4}-\dfrac{3}{4}\)

\(=\dfrac{-15}{4}\)