Ta có công thức:
\(\frac{a}{c.\left[c+1\right].\left[c+2\right]}=\frac{a}{2}\left[\frac{1}{c.\left[c+1\right]}-\frac{1}{\left[c+1\right].\left[c+2\right]}\right]\)
vậy
\(C=\frac{1}{2}\left[\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+.....+\frac{1}{11.12}-\frac{1}{12.13}\right]\)
\(C=\frac{1}{2}\left[\frac{1}{1.2}-\frac{1}{12.13}\right]\)
\(C=\frac{1}{2}.\frac{77}{156}=\frac{77}{312}\)
mình làm đầu tiên đó,
Chúc bạn học tốt !
\(C=\frac{1}{1.2.3}+\frac{1}{2.3.4}+...+\frac{1}{11.12.13}\)
\(=\frac{1}{2}\left(\frac{1}{1.2}-\frac{1}{2.3}+\frac{1}{2.3}-\frac{1}{3.4}+...+\frac{1}{11.12}-\frac{1}{12.13}\right)\)
\(=\frac{1}{2}\left(\frac{1}{2}-\frac{1}{156}\right)\)
\(=\frac{1}{2}\cdot\frac{77}{156}\)
\(=\frac{77}{312}\)
