Rút gọn bằng kiểu nào?
\(P=\frac{5}{3\cdot7}+\frac{5}{7\cdot11}+\frac{5}{11\cdot15}+...+\frac{5}{\left(4n-1\right)\left(4n+3\right)}\)
\(P=\frac{5}{4}\left(\frac{4}{3\cdot7}+\frac{4}{7\cdot11}+\frac{4}{11\cdot15}+...+\frac{4}{\left(4n-1\right)\left(4n+3\right)}\right)\)
\(P=\frac{5}{4}\left(\frac{1}{3}-\frac{1}{7}+\frac{1}{7}-\frac{1}{11}+...+\frac{1}{4n+3}\right)\)
\(P=\frac{5}{4}\left(\frac{1}{3}-\frac{1}{4n+3}\right)\)
...
P=\(\frac{5}{3x7}\) +\(\frac{5}{7x11}\)+\(\frac{5}{11x15}\)+...+\(\frac{5}{\left(4n-1\right)x\left(4n+3\right)}\)
\(\frac{4}{5}\)P=\(\frac{4}{3x7}\)+\(\frac{4}{7x11}\)+\(\frac{4}{11x15}\)+...+\(\frac{4}{\left(4n-1\right)x\left(4n+3\right)}\)
\(\frac{4}{5}\)P=\(\frac{1}{3}\)-\(\frac{1}{7}\)+\(\frac{1}{7}\)-\(\frac{1}{11}\)+...+\(\frac{1}{4n-1}\)-\(\frac{1}{4n+3}\)
\(\frac{4}{5}\)P=\(\frac{1}{3}\)-\(\frac{1}{4n+3}\)
P=\(\frac{5}{12}\)-\(\frac{5}{16n+12}\)