Ta có:

\(\frac{1}{3.7}+\frac{1}{7.11}+\frac{1}{11.15}+...+\frac{1}{x.\left(x+4\right)}=\frac{5}{63}\)

\(=\frac{1}{4}.\left(\frac{4}{3.7}+\frac{4}{7.11}+\frac{4}{11.15}+...+\frac{4}{x.\left(x+4\right)}\right)=\frac{5}{63}\)

\(\Rightarrow\left(\frac{1}{3}-\frac{1}{7}+\frac{1}{7}-\frac{1}{11}+\frac{1}{11}-\frac{1}{15}+....+\frac{1}{x}-\frac{1}{x+4}\right)=\frac{5}{63}:\frac{1}{4}\)

\(\Rightarrow\frac{1}{3}-\frac{1}{x+4}=\frac{20}{63}\Leftrightarrow\frac{1}{x+4}=\frac{1}{63}\Leftrightarrow x=63-4=59\)

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=\(\frac{5}{12}\)-\(\frac{5}{16n+12}\)

\(A=\frac{4}{3X7}+\frac{4}{7X11}+\frac{4}{11X15}+...+\frac{4}{100X104}\)

\(=\frac{1}{3}-\frac{1}{7}+\frac{1}{7}-\frac{1}{11}+\frac{1}{11}-\frac{1}{15}+...+\frac{1}{100}-\frac{1}{104}\)

\(=\frac{1}{3}-\frac{1}{104}\)

\(=\frac{101}{312}\)

Chúc bạn học giỏi nha!!!

K cho mik với nhé nguyen huu thuong 2005

\(A=\frac{4}{3.7}+\frac{4}{7.11}+\frac{4}{11.15}+...+\frac{4}{100.104}\)

\(A=\frac{1}{3}-\frac{1}{7}+\frac{1}{7}-\frac{1}{11}+\frac{1}{11}-\frac{1}{15}+...+\frac{1}{100}-\frac{1}{104}\)

\(A=\frac{1}{3}-\frac{1}{104}=\frac{104}{312}-\frac{3}{312}=\frac{101}{312}\)

A=4/3.7 +4/7.11 +4/11.15 +...+4/100.104 

A=1/3 −1/7 +1/7 −1/11 +1/11 −1/15 +...+1/100 −1/104 

A=1/3 −1/104 =104/312 −3/312 =101/312 

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=\(\frac{11}{141}\)

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