Question

tinh x=1/3+1/6+1/10+....+2/x (x+1)

Answer 1

ai nhanh minh k cho

Answer 2

\(x=\frac{1}{3}+\frac{1}{6}+........+\frac{2}{x\left(x+1\right)}\)

\(=\frac{2}{6}+\frac{2}{12}+.........+\frac{2}{x\left(x+1\right)}\)

\(=2\left(\frac{1}{2.3}+\frac{1}{3.4}+......+\frac{1}{x\left(x+1\right)}\right)\)

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

\(=2\left(\frac{1}{2}-\frac{1}{x}\right)\)

\(=1-\frac{2}{x}\)

\(\Leftrightarrow x=\frac{x}{x}-\frac{2}{x}\)

\(\Leftrightarrow x-2=x^2\)