Đặt \(A=\frac{1}{1.2.3}+\frac{1}{3.5.7}+...+\frac{1}{45.47.49}\)
\(\Rightarrow4A=\frac{4}{1.3.5}+\frac{4}{3.5.7}+...+\frac{4}{45.47.49}\)
\(=\frac{1}{1.3}-\frac{1}{3.5}+\frac{1}{3.5}-\frac{1}{5.7}+...+\frac{1}{45.47}-\frac{1}{47.49}\)
\(=\frac{1}{3}-\frac{1}{47.49}\)
\(\Rightarrow A=\frac{\frac{1}{3}-\frac{1}{47.49}}{4}=\frac{575}{6909}\)
Giúp mình với!!!!!
Tính:
G=\(\frac{1}{1\times3\times5}+\frac{1}{5\times7\times9}+\frac{1}{9\times11\times13}+...+\frac{1}{49\times51\times53}\)
C= \(\frac{3}{3\times5}+\frac{3}{5\times7}+\frac{3}{7\times9}+....+\frac{3}{47\times49}\)
\(\frac{1}{2\times3}+\frac{1}{3\times4}+\frac{1}{4\times5}+\frac{1}{5\times6}+\frac{1}{6\times7}+\frac{1}{7\times8}+\frac{1}{8\times9}+\frac{1}{9\times10}\)
Tính : \(\frac{1}{3\times5}+\frac{1}{5\times7}+\frac{1}{7\times9}...+\frac{1}{2009\times2011}\)
\(a=\frac{1}{3\times5}+\frac{1}{5\times7}+\frac{1}{7\times9}+......+\frac{1}{2003\times2005}\)
tính: \(\frac{1}{1\times3}+\frac{1}{3\times5}+\frac{1}{5\times7}+....+\frac{1}{2009\times2011}\)
\(\frac{2^5\times7+2^5}{2^5\times5^2-2^5\times3}\)
Help me!!!
\(\frac{1}{3\times5}+\frac{1}{5\times7}+\frac{1}{7\times9}+...+\frac{1}{\left(2x+1\right)\left(2x+3\right)}=\frac{15}{96}\)
\(\frac{7}{1\times3}+\frac{7}{3\times5}+\frac{7}{5\times7}+......+\frac{7}{99\times101}\)
