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\(A=\frac{2}{3\cdot5}+\frac{2}{5\cdot7}+...+\frac{2}{17\cdot19}\)
\(A=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{17}-\frac{1}{19}\)
\(A=\frac{1}{3}-\frac{1}{19}\)
\(A=\frac{16}{57}\)
Dấu "." là dấu nhân nhá ^^
\(\frac{2}{3\times5}+\frac{2}{5\times7}+...+\frac{2}{17\times19}=\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{17}-\frac{1}{19}\)
=\(\frac{1}{3}-\frac{1}{19}=\frac{19}{57}-\frac{3}{57}=\frac{19-3}{57}=\frac{16}{57}\)
\(\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+....+\frac{1}{x\left(x+2\right)}=\frac{8}{17}\)
\(\Leftrightarrow2\left(\frac{1}{1.3}+\frac{1}{3.5}+\frac{1}{5.7}+....+\frac{1}{x\left(x+2\right)}\right)=2.\frac{8}{17}\)
\(\Leftrightarrow\frac{2}{1.3}+\frac{2}{3.5}+\frac{2}{5.7}+....+\frac{2}{x\left(x+2\right)}=\frac{16}{17}\)
\(\Leftrightarrow1-\frac{1}{3}+\frac{1}{3}-\frac{1}{5}+....+\frac{1}{x}-\frac{1}{x+2}=\frac{16}{17}\)
\(\Leftrightarrow1-\frac{1}{x+2}=\frac{16}{17}\)
\(\Leftrightarrow\frac{1}{x+2}=1-\frac{16}{17}=\frac{1}{17}\)
\(\Rightarrow x+2=17\Rightarrow x=15\)
Tìm x:
\(\left(\frac{1}{3x5}+\frac{1}{5x7}+\frac{1}{7x9}+.....+\frac{1}{19x21}\right).x=\frac{9}{7}\)
\(\left(\frac{1}{3.5}+\frac{1}{5.7}+\frac{1}{7.9}+...+\frac{1}{19.21}\right)x=\frac{9}{7}\)
\(\left[\frac{1}{2}\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+\frac{1}{7}-\frac{1}{9}+...+\frac{1}{19}-\frac{1}{21}\right)\right]x=\frac{9}{7}\)
\(\left[\frac{1}{2}\left(\frac{1}{3}-\frac{1}{21}\right)\right]x=\frac{9}{7}\)
\(\left(\frac{1}{2}.\frac{2}{7}\right)x=\frac{9}{7}\)
\(\frac{1}{7}.x=\frac{9}{7}\)
\(x=\frac{9}{7}\div\frac{1}{7}\)
\(x=9\)
Vậy ...
Theo cách mk học sẽ suy ra lun
=1/1-1/3+1/3-1/5+1/5-1/7+...+1/2001-1/2003+1/2003-1/2005
=1-1/2005
=2004/2005
\(\left(\frac{2}{11.13}+\frac{2}{13.15}+...+\frac{2}{19.21}\right).462-x=19\)
\(\left(\frac{1}{11}-\frac{1}{13}+...+\frac{1}{19}-\frac{1}{21}\right)\cdot462-x=19\)
\(\left(\frac{1}{11}-\frac{1}{21}\right)\cdot462-x=19\)
\(\frac{10}{231}.462-x=19\)
\(20-x=19\)
\(x=20-19\)
\(x=1\)
Đề abfi sai. Chỗ đó là 19, k phải 29
Bạn biết tính chất này không?
\(\frac{a}{n\left(n+a\right)}=\frac{1}{n}-\frac{1}{n+a}\)
Sử dụng tính chất đó thì được:
\(\left(\frac{2}{11}-\frac{2}{13}+\frac{2}{13}-\frac{2}{15}+...+\frac{2}{19}-\frac{2}{21}\right)\)x 462 - x =19
\(\left(\frac{2}{11}-\frac{2}{21}\right)\cdot462-x=19\)
\(\frac{924}{11}-\frac{924}{21}-x=19\)
84 - 44 - x =19
40 - x = 19
x = 40 - 19
x = 21
Nhớ tk cho mình nếu đúng nhé
1. \(\left(\frac{2}{11.13}+\frac{2}{13.15}+\frac{2}{15.17}+\frac{2}{17.19}+\frac{2}{19.21}\right)\times462-x=19\)
\(\left(\frac{13-11}{11.13}+\frac{15-13}{13.15}+\frac{17-15}{15.17}+\frac{19-17}{17.19}+\frac{21-19}{19.21}\right)\times462-x=19\)
\(\left(\frac{1}{11}-\frac{1}{13}+\frac{1}{13}-\frac{1}{15}+\frac{1}{15}-\frac{1}{17}+\frac{1}{17}-\frac{1}{19}+\frac{1}{19}-\frac{1}{21}\right)\times462-x=19\)
\(\left(\frac{1}{11}-\frac{1}{21}\right)\times462-x=19\)
\(\frac{10}{231}\times462-x=19\)
\(20-x=19\)
\(x=20-19\)
\(x=1\)
2.b \(187-[[497-(8\times x+11)\div x]\div3-78]=150\)
\(187-[[497-(\frac{8\times x}{x}+\frac{11}{x})]:3-78]=150\)
\(187-[(497-8-\frac{11}{x}):3-78]=150\)
\(187-[(489-\frac{11}{x}):3-78]=150\)
\(187-[\frac{489}{3}-\frac{33}{x}-78]=150\)
\(187-[163-\frac{33}{x}-78]=150\)
\(187-85+\frac{33}{x}=150\)
\(102+\frac{33}{x}=150\)
\(\frac{33}{x}=150-102\)
\(\frac{33}{x}=48\)
\(x=\frac{48}{33}=\frac{16}{11}\)
\(\left(\frac{2}{3\times5}+\frac{2}{5\times7}+...+\frac{2}{17\times19}\right)\times57-2\times\left(x-1\right)=10\)
\(\left(\frac{1}{3}-\frac{1}{5}+\frac{1}{5}-\frac{1}{7}+...+\frac{1}{17}-\frac{1}{19}\right)\times57-2\times\left(x-1\right)=10\)
\(\left(\frac{1}{3}-\frac{1}{19}\right)\times57-2\times\left(x-1\right)=10\)
\(\frac{16}{57}\times57-2\times\left(x-1\right)=10\)
\(16-2\times\left(x-1\right)=10\)
\(2\times\left(x-1\right)=16-10\)
\(2\times\left(x-1\right)=6\)
\(x-1=6:2\)
\(x-1=3\)
\(x=3+1\)
\(x=4\)