Question

[Lê Quỳnh Hương]

\(\frac{1}{3}+\frac{1}{6}+\frac{1}{10}+............+\frac{2.x}{x.\left(x+1\right)}=\frac{2005}{2017}\)

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Answer 1

[♨❤♨~Koo ๖ۣۜϑũ❥꧁şɦυυ꧂❣ ♫✔♫]

Đặt N=\(\frac{1}{3}\)+\(\frac{1}{6}\)+\(\frac{1}{10}\)+......+\(\frac{2x}{x\left(x+1\right)}\)

N=\(\frac{2}{6}\)+\(\frac{2}{12}\)+\(\frac{2}{20}\)+.....+\(\frac{2x}{x\left(x+1\right)}\)

N=\(\frac{2}{2.3}\)+\(\frac{2}{3.4}\)+\(\frac{2}{4.5}\)+.....+\(\frac{2x}{x\left(x+1\right)}\)