Question

1/5x6x7+1/6x7x8+...+1/18x19x20

Answer 1

\(\dfrac{1}{5x6x7}+\dfrac{1}{6x7x8}+...+\dfrac{1}{18x19x20}\)

= \(\dfrac{1}{2}x\left(\dfrac{7-5}{5x6x7}+\dfrac{8-6}{6x7x8}+...+\dfrac{20-18}{18x19x20}\right)\)

= \(\dfrac{1}{2}x\left(\dfrac{1}{5x6}-\dfrac{1}{6x7}+\dfrac{1}{6x7}-\dfrac{1}{7x8}+...+\dfrac{1}{18x19}-\dfrac{1}{19x20}\right)\)

= \(\dfrac{1}{2}x\left(\dfrac{1}{5x6}-\dfrac{1}{19x20}\right)\)

= \(\dfrac{1}{2}x\left(\dfrac{1}{30}-\dfrac{1}{380}\right)\)

* Tự tính típ nha ! Mình mất cái máy tính ==" . Dấu \(x\) là nhân nha