Question

Tính nhanh

1/2+-1/3+1/4+-1/5+1/6+-1/7+-1/6+1/5+-1/4+1/3+-1/2

Answer 1

\(\dfrac{1}{2}+\left(-\dfrac{1}{3}\right)+\dfrac{1}{4}+\left(-\dfrac{1}{5}\right)+...+\dfrac{1}{5}+\left(-\dfrac{1}{4}\right)+\dfrac{1}{3}+\left(-\dfrac{1}{2}\right)\)\(+\left(-\dfrac{1}{7}\right)\)

\(=\left[\dfrac{1}{2}+\left(-\dfrac{1}{2}\right)\right]+\left[\dfrac{1}{3}+\left(-\dfrac{1}{3}\right)\right]+\left[\dfrac{1}{4}+\left(-\dfrac{1}{4}\right)\right]+...+\left[\dfrac{1}{6}+\left(-\dfrac{1}{6}\right)\right]\)

\(+\left(-\dfrac{1}{7}\right)\)

\(=0-\dfrac{1}{7}=-\dfrac{1}{7}\)