Ta có : \(\frac{3}{1.3}+\frac{3}{3.5}+\frac{3}{5.7}+......+\frac{3}{49.51}\)
\(=\frac{3}{2}\left(\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+......+\frac{2}{49.51}\right)\)
\(=\frac{3}{2}\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+......+\frac{1}{49}-\frac{1}{50}\right)\)
\(=\frac{3}{2}\left(1-\frac{1}{50}\right)\)
\(=\frac{3}{2}.\frac{49}{50}=\frac{147}{100}\)
Bài 1 dùng máy tính Casio bấm là ra.
cau 1
3/1x3+3/3x5+...+3/49x51
=2/3x(2/1x3+2/3x5+...+2/49x511)
=2/3x(1-1/3+1/3-1/5+...+1/49-1/51)
=2/3x(1-1/51)
=2/3x50/51
=100/153
\(\frac{3}{1.3}+\frac{3}{3.5}+\frac{3}{5.7}+\frac{3}{7.9}+...+\frac{3}{49.51}\)
= \(3.\left(\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+...+\frac{1}{49.51}\right)\)
=.\(3.2\left(\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+...+\frac{1}{49.51}\right)\)
=\(3.\left(\frac{2}{1.2}+\frac{2}{3.5}+\frac{2}{5.7}+\frac{2}{7.9}+...+\frac{2}{49.51}\right)\)
=\(3.\left(1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{49}-\frac{1}{51}\right)\)
=\(3.\left(1-\frac{1}{51}\right)\)
=\(3.\left(\frac{51}{51}-\frac{1}{51}\right)\)
=\(3.\frac{50}{51}\)
=\(\frac{50}{17}\)
