tính nhanh 1/2+-1/3+1/4+-1/5+1/6+-1/7+1/8 +1/7+-1/6+1/5+-1/4+1/3+-1/2

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1. 1/2 + (-1/3) + 1/4 + (-1/5) + 1/6 + (-1/7) + 1/8 + 1/7 + (-1/6) + 1/5 + (-1/4) +1/3 + (-1/2)

   = 1/2 – 1/2 -1/3 + 1/3 +1/4 – 1/4 -1/5 + 1/5 +1/6 – 1/6 – 1/7 + 1/7 + 1/8

   = 1/8

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2. $\dfrac{1}{2}+\dfrac{-1}{3}+\dfrac{1}{4}+\dfrac{-1}{5}+\dfrac{1}{6}+\dfrac{-1}{7}+\dfrac{1}{8}+\dfrac{1}{7}+\dfrac{-1}{6}+\dfrac{1}{5}+\dfrac{-1}{4}+\dfrac{1}{3}+\dfrac{-1}{2}$

   $=\left[\left(\dfrac{1}{2}+\dfrac{-1}{2}\right)+\left(\dfrac{-1}{3}+\dfrac{1}{3}\right)+\left(\dfrac{1}{4}+\dfrac{-1}{4}\right)+\left(\dfrac{-1}{5}+\dfrac{1}{5}\right)+\left(\dfrac{1}{6}+\dfrac{-1}{6}\right)+\left(\dfrac{-1}{7}+\dfrac{1}{7}\right)\right]+\dfrac{1}{8}$

   $= [0+0+0+0+0+0]+\dfrac{1}{8}$

   $=0+\dfrac{1}{8}$

   $=\dfrac{1}{8}$

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