Question

tính bằng cách nhanh nhất

2/15 + 2/35 + 2/63 + 2/99 + 32/143 + 2/195

Answer 1

2/15 + 2/35 + 2/63 + 2/99 + 2/143 + 2/195

\(=2\times\left(\dfrac{1}{3.5}+\dfrac{1}{5.7}+\dfrac{1}{7.9}+\dfrac{1}{9.11}+\dfrac{1}{11.13}+\dfrac{1}{13.15}\right)\)

= \(2\times\left(\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{11}+\dfrac{1}{11}-\dfrac{1}{13}+\dfrac{1}{13}-\dfrac{1}{15}\right)\)

\(=2\times\left(\dfrac{1}{3}-\dfrac{1}{15}\right)\)

\(=2\times\dfrac{4}{15}\)

\(=\dfrac{8}{15}\)