Question

\(\frac{1}{1x2}\)+\(\frac{1}{2x3}\)+\(\frac{1}{3x4}\)+...+\(\frac{1}{yx\left(y+1\right)}\)=\(\frac{996}{997}\)

Ai nhanh mình tick nè !

 

Answer 1

\(\frac{1}{1\times2}+\frac{1}{2\times3}+\frac{1}{3\times4}+...+\frac{1}{y\times\left(y+1\right)}=\frac{996}{997}\)

\(\Leftrightarrow1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+....+\frac{1}{y}-\frac{1}{y+1}=\frac{996}{997}\)

\(\Leftrightarrow1-\frac{1}{y+1}=\frac{996}{997}\)

\(\Leftrightarrow\frac{1}{y+1}=1-\frac{996}{997}=\frac{1}{997}\)

\(\Leftrightarrow y+1=997\Leftrightarrow y=996\)

Vậy y = 996

Answer 2

1/1×2 + 1/2×3 + 1/3×4 + ... + 1/ y x (y+1) =996/997

1-1/2+1/2-1/3+1/3-1/4+...+1/y - 1/y+1 =996/997

1-1/y+1=996/997

1/ y+1 =1-996/997

1/y+1 = 997/997-996/997

1/y+1=1/997

=> y+1 =997

y=997-1

y=996

Vậy y = 996