Question

\(\frac{3}{5x7}\)+ \(\frac{3}{7x9}\)+ \(\frac{3}{9x11}\)+ ... + \(\frac{3}{2013x2015}\)

Đây là bài tính nhanh, giúp mk nhé

Answer 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 \(\frac{3}{5\cdot7}+\frac{3}{7\cdot9}+\frac{3}{9\cdot11}+...+\frac{3}{2013\cdot2015}=\frac{603}{2015}\)

Answer 2

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!!!

Answer 3

    \(\frac{3}{5\text{×}7}+\frac{3}{7\text{×}9}+.......+\frac{3}{2013\text{×}2015}\)

\(=\frac{3}{2}\text{×}\left(\frac{2}{5\text{×}7}+\frac{2}{7\text{×}9}+........+\frac{2}{2013\text{×}2015}\right)\)

\(=\frac{3}{2}\text{×}\left(\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+......+\frac{1}{2013}-\frac{1}{2015}\right)\)

\(=\frac{3}{2}\text{×}\left(\frac{1}{5}-\frac{1}{2015}\right)\)

\(=\frac{3}{2}\text{×}\frac{402}{2015}\)

\(=\frac{603}{2015}\)

Answer 4

\(\frac{3}{5\cdot7}+\frac{3}{7\cdot9}+\frac{3}{9\cdot11}+...+\frac{3}{2013\cdot2015}\)

\(=\frac{3}{2}\cdot\left(\frac{2}{5\cdot7}+\frac{2}{7\cdot9}+\frac{2}{9\cdot11}+...+\frac{2}{2013\cdot2015}\right)\)

\(=\frac{3}{2}\left(\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+\frac{1}{9}-\frac{1}{11}+...+\frac{1}{2013}-\frac{1}{2015}\right)\)

\(=\frac{3}{2}\left(\frac{1}{5}-\frac{1}{2015}\right)\)

\(=\frac{3}{2}\cdot\frac{402}{2015}\)

\(=\frac{603}{2015}\)