Question

\(\dfrac{1}{\begin{matrix}1\times&2\end{matrix}}+\dfrac{1}{\begin{matrix}2\times&3\end{matrix}}+\dfrac{1}{\begin{matrix}3\times&4\end{matrix}}+...........+\dfrac{1}{x\times\left(x+1\right)}=\dfrac{996}{997}\)

Answer 1

đáp số là 996 đúng ko

Answer 2

\(\dfrac{1}{1.2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+...+\dfrac{1}{x\left(x+1\right)}=\dfrac{996}{997}\)

\(1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{4}+...+\dfrac{1}{x}-\dfrac{1}{x+1}\)= \(\dfrac{996}{997}\) \(1-\dfrac{1}{x+1}\) = \(\dfrac{996}{997}\)

\(\dfrac{1}{x+1}\) = \(1-\dfrac{996}{997}\)

\(\dfrac{1}{x+1}\) =\(\dfrac{1}{997}\)

\(\Rightarrow\) x + 1 = 997

x = 997 - 1

x = 996

Vậy x = 996