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\(\frac{2}{3\cdot5}+\frac{2}{5\cdot7}+\frac{2}{7\cdot9}+...+\frac{2}{99\cdot101}\)
\(=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{99}-\frac{1}{101}\)
\(=\frac{1}{3}-\frac{1}{101}\)
\(=\frac{98}{303}\)
Tích mk nha bn !!!! ^_^
\(\frac{2^2}{1x3}\)x \(\frac{4^2}{3x5}\)x \(\frac{6^2}{5x7}\) x \(\frac{8^2}{7x9}\)
= \(\frac{4}{3}\)x \(\frac{16}{15}\)x \(\frac{36}{35}\)x \(\frac{64}{63}\)
= \(1.486077098\)
a) Ta có: \(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+...+\frac{2}{11.13}=1\text{-}\frac{1}{3}+\frac{1}{3}\text{-}\frac{1}{5}+...+\frac{1}{11}\text{-}\frac{1}{13}=1\text{-}\frac{1}{13}=\frac{12}{13}\)
Thay vào ta có:
\(\frac{12}{13}+x=\frac{24}{13}\Rightarrow x=\frac{24}{13}\text{-}\frac{12}{13}\Rightarrow x=\frac{12}{13}\)
\(\left(\frac{2}{11.13}+\frac{2}{13.15}+\frac{2}{15.17}+\frac{2}{17.19}+\frac{2}{19.21}\right)\cdot462-x=19\)
\(\Rightarrow\left(\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}+...+\frac{1}{19}-\frac{1}{21}\right)\cdot462-x=19\)
\(\Rightarrow\left(\frac{1}{11}-\frac{1}{21}\right)\cdot462-x=19\)
\(\Rightarrow\frac{10}{231}\cdot462-x=19\)
\(\Rightarrow20-x=19\Rightarrow x=1\)
Ta có:
\(\left(\frac{2}{11.13}+\frac{2}{13.15}+\frac{2}{15.17}+\frac{2}{17.19}+\frac{2}{19.21}\right).462-x=19\)
\(\Rightarrow\left(\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}+\frac{1}{15}-\frac{1}{17}+\frac{1}{17}-\frac{1}{19}+\frac{1}{19}-\frac{1}{21}\right).462-x=19\)
\(\Rightarrow\left(\frac{1}{11}-\frac{1}{21}\right).462-x=19\)
\(\Rightarrow\frac{10}{231}.462-x=19\Leftrightarrow20-x=19\)
\(\Rightarrow x=20-19=1\)
\(\frac{3}{5\cdot7}+\frac{3}{7\cdot9}+\frac{3}{9\cdot11}+...+\frac{3}{2013\cdot2015}\)
\(=\frac{3}{2}\cdot\left(\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}+...+\frac{1}{2013}-\frac{1}{2015}\right)\)
\(=\frac{3}{2}\cdot\left(\frac{1}{5}-\frac{1}{2015}\right)=\frac{3}{2}\cdot\frac{402}{2015}-\frac{603}{2015}\)
Vậy \(\frac{3}{5\cdot7}+\frac{3}{7\cdot9}+\frac{3}{9\cdot11}+...+\frac{3}{2013\cdot2015}=\frac{603}{2015}\)
3/5.7 + 3/7.9 + 3/9.11 + ... 3/2013.2015
= 3/2.( 2/5.7 + 2/7.9 + 2/9.11 + ... + 2/2013.2015)
= 3/2. ( 1/5 - 1/7 + 1/7 - 1/9 + 1/9 - 1/11 + ... + 1/2013 - 1/2015)
~~~ SAU ĐÓ BẠN GẠCH ĐI NHỮNG PHÂN SỐ GIỐNG NHAU NHÁ ~~~
= 3/2. ( 1/5 - 1/2015)
= 3/2. 2010/10075
= 603/4030
Mk chắc chắn cách làm đúng đó!!!
\(\frac{2}{3\cdot5}+\frac{2}{5\cdot7}+\frac{2}{7\cdot9}+\frac{2}{9\cdot11}+\frac{2}{11\cdot13}+\frac{2}{13\cdot15}\)
\(=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}+\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}\)
\(=\frac{1}{3}-\frac{1}{15}\)
\(=\frac{4}{15}\)
Chúc bn hok giỏi !!!!!!!!! ^_^