Question

\(\frac{6}{1x3}\)+\(\frac{6}{3x5}\)+\(\frac{6}{5x7}\)+ .............+ \(\frac{6}{35x37}\)+\(\frac{6}{37x39}\)

 tính bằng cách thuận tiện 

Answer 1

1/2 x (6/1-6/3+6/3-6/5+ ... +6/37-6/39)

1/2 x (6/1-6/39)

1/2 x 228/39

228/78

Answer 2

\(\frac{6}{1\cdot3}+\frac{6}{3.5}+\frac{6}{5.7}+...+\frac{6}{35.37}+\frac{6}{37.39}\) 

\(=3\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{37}-\frac{1}{39}\right)\) 

\(=3\left(1-\frac{1}{39}\right)=3\cdot\frac{38}{39}=\frac{114}{39}\) 

Ps: Bạn tự rút gọn nhé!!!

Answer 3

\(\frac{6}{1.3}+\frac{6}{3.5}+...+\frac{6}{35.37}+\frac{6}{37.39}\)

\(=3\left(\frac{2}{1.3}+\frac{2}{3.5}+...+\frac{2}{35.37}+\frac{2}{37.39}\right)\)

\(=3\left(\frac{1}{1}-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+...+\frac{1}{37}-\frac{1}{39}\right)\)

\(=3\left(1-\frac{1}{39}\right)\)

\(=3.\frac{38}{39}\)

\(=\frac{38}{13}\)