\(A=\frac{1}{3\cdot5}+\frac{1}{5\cdot7}+...+\frac{1}{55\cdot57}\)
\(2A=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{55}-\frac{1}{57}\)
\(2A=\frac{1}{3}-\frac{1}{57}\)
\(2A=\frac{6}{19}\)
\(A=\frac{3}{19}\)
Ta có:
A=1/15+1/35+1/63+1/99+...+1/2015+1/3135
=1/3.5+1/5.7+1/7.9+1/9.11+...+1/45.47+1/47.49
=1/3-1/5+1/5-1/7+1/7-1/9+...+1/45-1/47+1/47-1/49
=1/3-1/49
=49/147-3/147
=47/147
\(A=\frac{1}{12}+\frac{1}{35}+\frac{1}{63}+\frac{1}{99}+...+\frac{1}{2015}+\frac{1}{3135}\)
\(A=\frac{1}{3\cdot5}+\frac{1}{5\cdot7}+\frac{1}{7\cdot9}+\frac{1}{9\cdot11}+...+\frac{1}{45\cdot47}+\frac{1}{47\cdot49}\)
\(A=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{47}-\frac{1}{49}\)
\(A=\frac{1}{3}-\frac{1}{49}\)
\(A=\frac{46}{147}\)
\(49-3=46\text{ nha bạn !}\)
