Question

Tính nhanh:

1/15 + 1/35 + 1/63 + 1/99 + 1/143 + 1/195

 

 

Answer 1

\(\dfrac{1}{15}+\dfrac{1}{35}+\dfrac{1}{63}+\dfrac{1}{99}+\dfrac{1}{143}+\dfrac{1}{195}\\ =\dfrac{1}{3\times5}+\dfrac{1}{5\times7}+\dfrac{1}{7\times9}+\dfrac{1}{9\times11}+\dfrac{1}{11\times13}+\dfrac{1}{13\times15}\\ =\dfrac{1}{2}\times\left(\dfrac{2}{3\times5}+\dfrac{2}{5\times7}+\dfrac{2}{7\times9}+\dfrac{2}{9\times11}+\dfrac{2}{11\times13}+\dfrac{2}{13\times15}\right)\\ =\dfrac{1}{2}\times\left(\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+...+\dfrac{1}{13}-\dfrac{1}{15}\right)\\ =\dfrac{1}{2}\times\left(\dfrac{1}{3}-\dfrac{1}{15}\right)\\ =\dfrac{1}{2}\times\dfrac{4}{15}\\ =\dfrac{2}{15}\)

Answer 2