\(A=\frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{\left(n-1\right)n}\)
\(=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{n-1}-\frac{1}{n}\)
\(=1-\frac{1}{n}\)
rút gọn \(B=\frac{5}{1\cdot2\cdot3}+\frac{5}{2\cdot3\cdot4}+....+\frac{5}{n\cdot\left(n+1\right)\left(n+2\right)}\)
\(\frac{1}{\sqrt{1\cdot2}}+\frac{1}{\sqrt{2\cdot3}}+\frac{1}{\sqrt{3\cdot4}}+...+\frac{1}{\sqrt{n\cdot\left(n+1\right)}}\)
rút gọn phân thức
TÍNH TỔNG:
\(\frac{1}{1\cdot2\cdot3}+\frac{1}{2\cdot3\cdot4}+\frac{1}{3\cdot4\cdot5}+.....+\frac{1}{n\left(n+1\right)\left(n+2\right)}\)
Rút gọn biểu thức : A= \(\frac{3}{\left(1\cdot2\right)^2}\) + \(\frac{5}{\left(2\cdot3\right)^2}\) + \(\frac{7}{\left(3\cdot4\right)^2}\) + .......+ \(\frac{2n+1}{\left[n\left(n+1\right)\right]^2}\)
Tính tổng của B :B=\(\frac{1}{1\cdot2\cdot3}+\frac{1}{2\cdot3\cdot4}+\frac{1}{3\cdot4\cdot5}+...+\frac{1}{n\left(n+1\right)\left(n+2\right)}\)
HD:\(\frac{1}{k\left(k+1\right)\left(k+2\right)}=\frac{1}{2}\left(\frac{1}{k}+\frac{1}{k+2}\right)-\frac{1}{k+1}\)
giải pt
\(\left(\frac{1}{1\cdot2\cdot3}+\frac{1}{2\cdot3\cdot4}+.......+\frac{1}{2005.2006.2007}\right)x=\left(1\cdot2+2\cdot3+.....+2006.2007\right)\)
(\(\left(\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+.......+\frac{1}{9\cdot10}\right)\left(x-1\right)+\frac{1}{10}x=x-\frac{9}{10}\)
Rút gọn biểu thức
\(A=\left(1-\frac{1}{2^2}\right).\left(1-\frac{1}{3^2}\right).\left(1-\frac{1}{4^2}\right)...\left(1-\frac{1}{n^2}\right)\)
Rút gọn \(A=\frac{3}{\left(1.2\right)^2}+\frac{5}{\left(2.3\right)^2}+\frac{7}{\left(3.4\right)^2}+...+\frac{2n+1}{\left[n\left(n+1\right)\right]^2}\)
