Đặt A=như đã cho.
=>1/2A=2/5*7+2/7*9+2/9*11+...+2/59*61.
=>1/2A=1/5-1/7+1/7-1/9+1/9-1/11+...+1/59-1/61.
=>1/2A=1/5-1/61=56/305.
=>A=56/305*2=112/305.
k nha đúng đó.Có j kb nha.
Ta có:
\(\frac{4}{5.7}+\frac{4}{7.9}+...+\frac{4}{59.61}\)
\(=2.\left(\frac{2}{5.7}+\frac{2}{7.9}+...+\frac{2}{59.61}\right)\)
\(=2.\left(\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{59}-\frac{1}{61}\right)\)
\(=2.\left(\frac{1}{5}-\frac{1}{61}\right)\)
\(=2.\frac{56}{305}=\frac{112}{305}\)
Ta có :
\(\frac{4}{5.7}+\frac{4}{7.9}+....+\frac{4}{59.61}\)
\(=2.\left(\frac{2}{5.7}+\frac{2}{7.9}+...+\frac{2}{59.61}\right)\)
\(=2.\left(\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+.......+\frac{1}{59}-\frac{1}{61}\right)\)
\(=2.\left(\frac{1}{5}-\frac{1}{61}\right)\)
\(=2.\frac{56}{305}=\frac{112}{305}\)
\(\frac{4}{5.7}+\frac{4}{7.9}+...+\frac{4}{59.61}\)
\(=2.\left(\frac{2}{5.7}+\frac{2}{7.9}+...+\frac{2}{59.61}\right)\)
\(=2.\left(\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{59}-\frac{1}{61}\right)\)
\(=2.\left(\frac{1}{5}-\frac{1}{61}\right)\)
\(=2.\frac{56}{305}\)
\(=\frac{102}{305}\)