=1/1*2+1/2*3+1/3*4+...+1*10*11+1/11*12=1-1/2+1/2-1/3+1/3-1/4+...+1/10-1/11+1/11-1/12
=1-1/12=11/12.
\(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{110}+\frac{1}{132}\)
\(=\frac{1}{1\times2}+\frac{1}{2\times3}+\frac{1}{3\times4}+...+\frac{1}{10\times11}+\frac{1}{11\times12}\)
\(=1-\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+....+\frac{1}{11}+\frac{1}{12}\)
\(=1-\frac{1}{12}\)
\(=\frac{11}{12}\)
\(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+...+\frac{1}{110}+\frac{1}{132}\)
\(=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{10.11}+\frac{1}{11.12}\)
\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{10}-\frac{1}{11}+\frac{1}{11}-\frac{1}{12}\)
\(=1-\frac{1}{12}\)
\(=\frac{11}{12}\)
k mình nha ! Chúc bạn học giỏi ! ^_^
\(\frac{1}{2}\)\(+\) \(\frac{1}{6}\) \(+\)\(\frac{1}{12}\) \(+\) \(\frac{1}{20}\) \(+\) \(...\) \(+\) \(\frac{1}{110}\) \(+\) \(\frac{1}{132}\)
\(=\) \(\frac{1}{1\times2}\) \(+\) \(\frac{1}{2\times3}\) \(+\) \(\frac{1}{3\times4}\) \(+\) \(\frac{1}{4\times5}\) \(+\) \(...\) \(+\) \(\frac{1}{10\times11}\)\(+\)\(\frac{1}{11\times12}\)
\(=\) \(1\) \(-\) \(\frac{1}{2}\) \(+\) \(\frac{1}{2}\) \(-\) \(\frac{1}{3}\) \(+\)\(\frac{1}{3}\) \(-\) \(\frac{1}{4}\) \(+\) \(\frac{1}{4}\) \(+\) \(...\) \(+\) \(\frac{1}{11}\) \(-\) \(\frac{1}{12}\)
\(=\) \(1\) \(-\) \(\frac{1}{12}\)
\(=\) \(\frac{11}{12}\)
Giải :
\(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+...+\frac{1}{110}+\frac{1}{132}\)
\(=\frac{1}{2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+...+\frac{1}{10.11}+\frac{1}{11.12}\)
\(=\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{10}-\frac{1}{11}+\frac{1}{11}-\frac{1}{12}\)
\(=\frac{1}{2}+\frac{1}{2}-\frac{1}{12}=1-\frac{1}{12}=\frac{11}{12}\)
