\(A=\frac{7}{1\cdot5}+\frac{7}{5\cdot9}+...+\frac{7}{17\cdot21}=\)
\(\frac{4}{7}A=\frac{4}{1\cdot5}+\frac{4}{5\cdot9}+...+\frac{4}{17\cdot21}=\)
\(\frac{4}{7}A=\left(1-\frac{1}{5}\right)+\left(\frac{1}{5}-\frac{1}{9}\right)+...+\left(\frac{1}{17}-\frac{1}{21}\right)=\)
\(\frac{4}{7}A=1-\frac{1}{21}=\)
\(\frac{4}{7}A=\frac{20}{21}\)
\(A=\frac{20}{21}\div\frac{4}{7}\)
\(A=\frac{20}{21}\times\frac{7}{4}=\frac{140}{84}=\frac{5}{3}\)
\(\frac{7}{1.5}+\frac{7}{5.9}+\frac{7}{9.13}+...+\frac{7}{17.21}\)
\(=\frac{7}{4}.\left(\frac{4}{1.5}+\frac{4}{5.9}+\frac{4}{9.13}+...+\frac{4}{17.21}\right)\)
\(=\frac{7}{4}.\left(1-\frac{1}{5}+\frac{1}{5}-\frac{1}{9}+...+\frac{1}{17}-\frac{1}{21}\right)\)
\(=\frac{7}{4}.\left(1-\frac{1}{21}\right)\)
\(=\frac{7}{4}.\frac{20}{21}=\frac{5}{3}\)
1/5 + 1/45 + 1/117 + 1/221 + 1/357+ .... + 1/159197
Đặt A=1/5 + 1/45 + 1/117 + 1/221 + 1/357+ .... + 1/159197
A= 1/1x5 + 1/5x9 + 1/9x13 + 1/13x17 + .... + 1/397x401
Ax4=4/1x5 + 4/5x9 + 4/9x13 + 4/13x17 + .... + 4/397x401
Ax4=(1-1/5) + (1/5-1/9) + (1/9-1/13)+….+(1/397-1/401)
Ax4=1-1/401
A=100/401
Mà 1/4=100/400>100/401=A nên A<1/4.
