\(C=\frac{1}{1.999}+\frac{1}{3.997}+...+\frac{1}{997.3}+\frac{1}{999.1}\)
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Tính giá trị biểu thức sau: \(C=\frac{1+\frac{1}{3}+\frac{1}{5}+...+\frac{1}{999}}{\frac{1}{1.999}+\frac{1}{3.997}+...+\frac{1}{997.3}+\frac{1}{999.1}}\)
\(ChoM=1+\frac{1}{3}+\frac{1}{5}+\frac{1}{7}+...+\frac{1}{999}\\ N=\frac{1}{1.999}+\frac{1}{3.997}+...+\frac{1}{997.3}+\frac{1}{999.1}\\ Tính\frac{M}{N}\)
\(N=\frac{1}{1.999}+\frac{1}{3.997}+...+\frac{1}{997.3}+\frac{1}{999.1}\)
\(1000N=1+\frac{1}{999}+\frac{1}{3}+\frac{1}{997}+...+\frac{1}{997}+\frac{1}{3}+1\)
\(1000N=2\left[1+\frac{1}{3}+\frac{1}{5}+...+\frac{1}{999}\right]\)
\(N=\frac{1}{50}\left[1+\frac{1}{3}+\frac{1}{5}+...+\frac{1}{999}\right]\)
\(\frac{M}{N}=\frac{1+\frac{1}{3}+\frac{1}{5}+...+\frac{1}{999}}{\frac{1}{50}\left[1+\frac{1}{3}+\frac{1}{5}+...+\frac{1}{999}\right]}=\frac{1}{\frac{1}{50}}=50\)
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Tính nhanh \(C=\frac{1+\frac{1}{3}+\frac{1}{5}+...+\frac{1}{999}}{\frac{1}{1.999}+\frac{1}{3.997}+...+\frac{1}{997.3}+\frac{1}{999.1}}\)
Giải chi tiết cho mk nha, thanks!
Làm thử thoi nhé :)
\(C=\frac{1+\frac{1}{3}+\frac{1}{5}+...+\frac{1}{999}}{\frac{1}{1.999}+\frac{1}{3.997}+...+\frac{1}{997.3}+\frac{1}{999.1}}\)
\(\frac{1}{1000}C=\frac{1+\frac{1}{3}+\frac{1}{5}+...+\frac{1}{999}}{\frac{1000}{1.999}+\frac{1000}{3.997}+...+\frac{1000}{997.3}+\frac{1000}{999.1}}\)
\(\frac{1}{1000}C=\frac{1+\frac{1}{3}+\frac{1}{5}+...+\frac{1}{999}}{\frac{1+999}{1.999}+\frac{3+997}{3.997}+...+\frac{997+3}{997.3}+\frac{999+1}{999.1}}\)
\(\frac{1}{1000}C=\frac{1+\frac{1}{3}+\frac{1}{5}+...+\frac{1}{999}}{\frac{1}{1.999}+\frac{999}{1.999}+\frac{3}{3.997}+\frac{997}{3.997}+...+\frac{997}{997.3}+\frac{3}{997.3}+\frac{999}{999.1}+\frac{1}{999.1}}\)
\(\frac{1}{1000}C=\frac{1+\frac{1}{3}+\frac{1}{5}+...+\frac{1}{999}}{\frac{1}{999}+\frac{1}{1}+\frac{1}{997}+\frac{1}{3}+...+\frac{1}{3}+\frac{1}{997}+\frac{1}{1}+\frac{1}{999}}\)
\(\frac{1}{1000}C=\frac{1+\frac{1}{3}+\frac{1}{5}+...+\frac{1}{999}}{2\left(1+\frac{1}{3}+\frac{1}{5}+...+\frac{1}{999}\right)}\)
\(\frac{1}{1000}C=\frac{1}{2}\)
\(C=\frac{1}{2}.1000\)
\(C=500\)
Vậy \(C=500\)
Chúc bạn học tốt ~
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Tính:
A= \(1+\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+......+\frac{1}{2^{2006}}\)
B= \(\frac{1+\frac{1}{3}+\frac{1}{5}+.....+\frac{1}{999}}{\frac{1}{1.999}+\frac{1}{3.997}+.....+\frac{1}{997.3}+\frac{1}{999.1}}\)
\(A=1+\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{2006}}\)
\(2A=2+1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^{2005}}\)
\(2A-A=\left(2+1+\frac{1}{2}+\frac{1}{2^2}+...+\frac{1}{2^{2005}}\right)-\left(1+\frac{1}{2}+\frac{1}{2^2}+\frac{1}{2^3}+...+\frac{1}{2^{2006}}\right)\)
\(A=2-\frac{1}{2^{2006}}\)
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\(\frac{1+\frac{1}{3}+\frac{1}{5}+.....+\frac{1}{999}}{\frac{1}{1.999}+\frac{1}{3.997}+....\frac{1}{997.3}+\frac{1}{991.1}}\)
\(=\frac{1000\left(1+\frac{1}{3}+\frac{1}{5}+...+\frac{1}{999}\right)}{1000\left(\frac{1}{1.999}+\frac{1}{3.997}+...+\frac{1}{997.3}+\frac{1}{999.1}\right)}=\frac{1000\left(1+\frac{1}{3}+\frac{1}{5}+...+\frac{1}{999}\right)}{\frac{1+999}{1.999}+\frac{3+997}{3.997}+...+\frac{997+3}{997.3}+\frac{999+1}{999.1}}\)
\(=\frac{1000\left(1+\frac{1}{3}+\frac{1}{5}+...+\frac{1}{999}\right)}{1+\frac{1}{999}+\frac{1}{3}+\frac{1}{997}+...+\frac{1}{997}+\frac{1}{3}+\frac{1}{999}+1}=\frac{1000\left(1+\frac{1}{3}+\frac{1}{5}+...+\frac{1}{999}\right)}{2\left(1+\frac{1}{3}+\frac{1}{5}+...+\frac{1}{999}\right)}=500\)
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Tính A=\(\frac{1+\frac{1}{3}+\frac{1}{5}+...+\frac{1}{999}}{\frac{1}{1.999}+\frac{1}{3.997}+...+\frac{1}{999.1}}\)
tính giá trị biểu thức 1/1.999+1/3.997+...+1/997.3+1/999.1
Đặt A=\(\frac{1}{1.999}+\frac{1}{3.997}+...+\frac{1}{3.997}+\frac{1}{1.999}\)
=>1000A=\(1+\frac{1}{999}+\frac{1}{3}+\frac{1}{997}+...+\frac{1}{997}+\frac{1}{3}+1=2\left(1+\frac{1}{3}+...+\frac{1}{997}+\frac{1}{999}\right)\)
=>A=\(\frac{1}{50}\left(1+\frac{1}{3}+...+\frac{1}{997}+\frac{1}{999}\right)\)
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Tính giá trị biểu thức :
B = -1/3 + 1/3^2 - 1/3^3 +.....+1/3^100 - 1/3^101
C = (1+1/3+1/5+...+1/999)/(1/1.999 + 1/3.997 + ... + 1/997.3 + 1/999.1)
Tìm x biết: frac{3}{2x+1}+ frac{10}{4x+2}- frac{6}{6x+3}frac{12}{26}Chứng minh rằng: frac{1}{5^2}+ frac{1}{6^2}+...+ frac{1}{2007^2} frac{1}{5}rút gọn: M ( 1+frac{1}{3}+ frac{1}{5}+ ... + frac{1}{999}) : (frac{1}{1.999}+ frac{1}{3.997}+...+frac{1}{997.3}+frac{1}{999.1})Giúp mình nha!!!
Đọc tiếp
Tìm x biết: \(\frac{3}{2x+1}\)+ \(\frac{10}{4x+2}\)- \(\frac{6}{6x+3}\)=\(\frac{12}{26}\)
Chứng minh rằng: \(\frac{1}{5^2}\)+ \(\frac{1}{6^2}\)+...+ \(\frac{1}{2007^2}\)> \(\frac{1}{5}\)
rút gọn: M = ( 1+\(\frac{1}{3}\)+ \(\frac{1}{5}\)+ ... + \(\frac{1}{999}\)) : (\(\frac{1}{1.999}\)+ \(\frac{1}{3.997}\)+...+\(\frac{1}{997.3}\)+\(\frac{1}{999.1}\))
Giúp mình nha!!!
\(\frac{3}{2x+1}+\frac{10}{4x+2}-\frac{6}{6x+3}=\frac{6}{13}\)
\(\Rightarrow\frac{3}{2x+1}+\frac{5}{2x+1}-\frac{2}{2x+1}=\frac{6}{13}\)
\(\Rightarrow\frac{6}{2x+1}=\frac{6}{13}\Rightarrow2x+1=13\Rightarrow x=6\)
mình giải hơi gọn có gì ko hiểu thì hỏi nha !
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