Question

Tìm x

1/3 + 1/6 + 1/10 + ....+ 2/ x(x + 1) = 2011/2013

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Answer 1

\(\Rightarrow\)\(\frac{2}{6}\)+ \(\frac{2}{12}\)+ \(\frac{2}{20}\)+...+\(\frac{2}{x\left(x+1\right)}\)= \(\frac{2011}{2013}\)

\(\Rightarrow\)\(\frac{2}{2.3}\)+ \(\frac{2}{3.4}\)+ \(\frac{2}{4.5}\)+...+  \(\frac{2}{x\left(x+1\right)}\)= \(\frac{2011}{2013}\)

\(\Rightarrow\)\(\frac{1}{2}\)- \(\frac{1}{3}\)+ \(\frac{1}{3}\)- \(\frac{1}{4}\)+...+ \(\frac{1}{x}\)- \(\frac{1}{x+1}\)= \(\frac{2011}{2013}\): 2

\(\Rightarrow\)\(\frac{1}{2}\)- \(\frac{1}{x+1}\)=  \(\frac{2011}{4026}\)

\(\Rightarrow\)\(\frac{1}{x+1}\)= \(\frac{1}{2}\)- \(\frac{2011}{4026}\)= \(\frac{1}{2013}\)

\(\Rightarrow\)\(x+1=2013\)

Answer 2

Bạn tự làm tiếp nha !