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M=1/3.7+1/7.11+1/11.15+...+1/43.47
M=1/3-1/7+1/7-1/11+1/11-1/15+...+1/43-1/47
M=1/3-1/47
CÒN LẠI TỰ TÍNH NHA BN
AI THẤY ĐÚNG THÌ ỦNG HỘ NHA
M=\(\frac{1}{3x7}+\frac{1}{7x11}+\frac{1}{11x15}+...+\frac{1}{43x47}\)
=>4M=\(\frac{4}{3x7}+\frac{4}{7x11}+...+\frac{4}{43x47}\)
=>4M=\(\frac{1}{3}-\frac{1}{7}+\frac{1}{7}-\frac{1}{11}+...+\frac{1}{43}-\frac{1}{47}\)
=>4M=\(\frac{1}{3}-\frac{1}{47}\)
=>4M=\(\frac{44}{141}\)
=>M=\(\frac{44}{141}:4\)
=>M=\(\frac{11}{141}\)
Mình lộn
S = \(\frac{\left(1+90\right)\times90\div2}{4}\)
S = \(\frac{4095}{4}\)
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=\(\frac{5}{12}\)-\(\frac{5}{16n+12}\)
\(A=\frac{4}{2}+\frac{4}{6}+\frac{4}{12}+\frac{4}{20}+\frac{4}{30}+\frac{4}{42}\)
\(A=\frac{4}{1.2}+\frac{4}{2.3}+\frac{4}{3.4}+\frac{4}{4.5}+\frac{4}{5.6}+\frac{4}{6.7}\)
\(A=4\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}\right)\)
\(A=4\left(1-\frac{1}{7}\right)\)
\(A=4.\frac{6}{7}\)
\(A=\frac{24}{7}\)
\(A=\frac{4}{2}+\frac{4}{6}+\frac{4}{12}+\frac{4}{20}+\frac{4}{30}+\frac{4}{42}=4\left(\frac{1}{2}+\frac{1}{6}+\frac{1}{12}+\frac{1}{20}+\frac{1}{30}+\frac{1}{42}\right)\)
\(=4\left(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+\frac{1}{4.5}+\frac{1}{5.6}+\frac{1}{6.7}\right)\)
\(=4\left(1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}+\frac{1}{6}-\frac{1}{7}\right)\)
\(=4\left(1-\frac{1}{7}\right)=\frac{6}{7}.4=\frac{24}{7}\)
4/42+4/56+4/72+4/90+4/110
=4*(1/42+1/56+1/72+1/90+1/110)
=4*(1/(6*7)+1/(7*8)+1/(8*9)+1/(9*10)+1/(10*11))
=4*(1/6-1/7+1/7-1/8+1/8-1/9+1/9-1/10+1/10-1/11)
=4*(1/6-1/11)
=4*5/66
=10/33
\(\frac{4}{6\cdot7}+\frac{4}{7\cdot8}+\frac{4}{8\cdot9}+\frac{4}{9\cdot10}+\frac{4}{10\cdot11}\)
\(4\cdot\left(\frac{1}{6\cdot7}+\frac{1}{7\cdot8}+\frac{1}{8\cdot9}+\frac{1}{9\cdot10}+\frac{1}{10\cdot11}\right)\)
\(4\cdot\frac{5}{66}\)
\(\frac{10}{33}\)
\(S=\frac{1}{4}+\frac{2}{4}+\frac{3}{4}+....+\frac{90}{4}\)
\(=\frac{1+2+3+...+90}{4}\)
\(=\frac{\frac{90\left(90+1\right)}{2}}{4}\)
\(=\frac{4095}{4}\)
\(\frac{1}{3}-\frac{1}{2027}\)