lớp 4 mà học dạng này rồi sao!?

\(\frac{12}{3\cdot7}+\frac{12}{7\cdot11}+...+\frac{12}{43\cdot47}=3\left(\frac{4}{3\cdot7}+\frac{4}{7\cdot11}+...+\frac{4}{43\cdot47}\right)=3\left(\frac{1}{3}-\frac{1}{7}+\frac{1}{7}-\frac{1}{11}+...+\frac{1}{43}-\frac{1}{47}\right)\)\(=3\left[\left(\frac{1}{3}-\frac{1}{47}\right)+\left(\frac{1}{7}-\frac{1}{7}\right)+...+\left(\frac{1}{43}-\frac{1}{43}\right)\right]=3\left[\left(\frac{47}{141}-\frac{3}{141}\right)+0+...+0\right]=3\cdot\frac{44}{141}=\frac{44}{47}\)

=\(3\cdot\left(\frac{4}{3\cdot7}+\frac{4}{7\cdot11}+...+\frac{12}{43\cdot47}\right)=3\left(\frac{1}{3}\left(\frac{1}{7}-\frac{1}{7}\right)-\left(\frac{1}{11}-\frac{1}{11}\right)-...-\frac{1}{47}\right)\)

=\(3\left(\frac{1}{3}-\frac{1}{47}\right)=3\cdot\frac{44}{141}=\frac{44}{47}\)

Nếu đúng cho xin lik nhé

Sao ko ai giup vây HuHu

?????

=12/3+12/11+12/15+..+12/43+12/47

=4+12/11+3/5+..+12/43+12/47

\(\frac{1}{3.7}+\frac{1}{7.11}+\frac{1}{11.15}+...+\frac{1}{31.35}+\frac{1}{35.39}\) ( . là nhân nhé )

\(=\frac{1}{4}.\left[4.\left(\frac{1}{3.7}+\frac{1}{4.11}+\frac{1}{11.15}+...+\frac{1}{31.35}+\frac{1}{35.39}\right)\right]\)

\(=\frac{1}{4}.\left(\frac{4}{3.7}+\frac{4}{7.11}+\frac{4}{11.15}+...+\frac{4}{31.35}+\frac{4}{35.39}\right)\)

\(=\frac{1}{4}.\left(\frac{1}{3}-\frac{1}{7}+\frac{1}{7}-\frac{1}{11}+\frac{1}{11}-\frac{1}{15}+...+\frac{1}{31}-\frac{1}{35}+\frac{1}{35}-\frac{1}{39}\right)\)

\(=\frac{1}{4}.\left(\frac{1}{3}-\frac{1}{39}\right)=\frac{1}{4}.\left(\frac{13-1}{39}\right)=\frac{1}{4}.\frac{12}{39}=\frac{1}{4}.\frac{4}{13}=\frac{1}{13}\)

cô giáo mik dạy thế đó. Mong bn hỉu bài này

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

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

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

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

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 

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

Ta có: \(\dfrac{4}{3\cdot7}+\dfrac{4}{7\cdot11}+\dfrac{4}{11\cdot15}+...+\dfrac{4}{23\cdot27}\)

\(=\dfrac{1}{3}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{11}+\dfrac{1}{11}-\dfrac{1}{15}+...+\dfrac{1}{23}-\dfrac{1}{27}\)

\(=\dfrac{1}{3}-\dfrac{1}{27}=\dfrac{8}{27}\)

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

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

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

Mình sửa lại đề một chút nhé.

\(\dfrac{4}{3\times7}+\dfrac{4}{7\times11}+\dfrac{4}{11\times15}+\dfrac{4}{15\times19}+\dfrac{4}{19\times23}+\dfrac{4}{23\times27}\)

\(=\dfrac{1}{3}-\dfrac{1}{7}+\dfrac{1}{7}-\dfrac{1}{11}+\dfrac{1}{11}-\dfrac{1}{15}+\dfrac{1}{15}-\dfrac{1}{19}+\dfrac{1}{19}-\dfrac{1}{23}+\dfrac{1}{23}-\dfrac{1}{27}\)

\(=\dfrac{1}{3}-\dfrac{1}{27}\)

\(=\dfrac{8}{27}\).

A = \(\dfrac{4}{3\times7}\) + \(\dfrac{4}{7\times11}\) + \(\dfrac{4}{11\times15}\) + \(\dfrac{4}{15\times19}\) + \(\dfrac{4}{19\times23}\) + \(\dfrac{4}{23\times27}\)

A =1/3 -1/7+1/7-1/11 + 1/11-1/15 + 1/15 - 1/19 + 1/19 -1/23+1/23-1/27

A = 1/3 - 1/27 

A = 8/27