Question

tim x biet

5/1.2 + 5/2.3 + 5/3.4 + …. 5/x(x+1) = 9998/9999

Answer 1

\(\frac{5}{1.2}+\frac{5}{2.3}+\frac{5}{3.4}+...+\frac{5}{x\left(x+1\right)}=\frac{9998}{9999}\)

\(\Leftrightarrow5\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{x}-\frac{1}{x+1}\right)=\frac{9998}{9999}\)

\(\Leftrightarrow5\left(1-\frac{1}{x+1}\right)=\frac{9998}{9999}\)

\(\Leftrightarrow1-\frac{1}{x+1}=\frac{9998}{9999}\div5\)

\(\Leftrightarrow1-\frac{1}{x+1}=\frac{9998}{49995}\)

\(\Leftrightarrow\frac{1}{x+1}=1-\frac{9998}{49995}=\frac{39997}{49995}\)

\(\Leftrightarrow x=\frac{9998}{39997}\)