1 Tính
A (1-1/2) * (1-1/3 ) * (1-1/4 ) * .....*(1-1/19)* ( 1-1/20)
B 3/2 * 4/3 * 6/5* ......* 2006/2005 * 2007/2006 * 2008/2007
Tính bằng cách nhanh nhất :
a. ( 1-1/2 ) x ( 1 -1/3) x ( 1-1/4) x.... x ( 1-18)x ( 1-1/19 ) x ( 1 - 1/20 )
b. 3/2 x 4/3 x 5/4 x ..... x 2006/2005 x 2007/2006 x 2008/2007
giải hộ mih nhé
a)=1/2*2/3......*19/20
=1/20
b)=3/2*4/3......*2008/2007
=3/2007
2008+2007/2+2006/3+2005/4+2005/5+........................3/2006+2/2007+1/2008
1/2+1/3+1/4+1/5+....................+1/2009
2008-1/2008=2007/2008
1/2-1/2009=2007/2009
2008+2007/2+2006/3+2005/4+2005/5+........................3/2006+2/2007+1/2008
1/2+1/3+1/4+1/5+....................+1/2009
Tính A/ B biết
A= 2008+ 2007/2 + 2006/3 + 2005/4+....+ 2/2007+ 1/2008 ; B = 1/2+1/3+1/4+1/5+....1/2008+1/2009
Cho: A= 1/2 + 1/3 + 1/4+ ... +1/2008
B= 2007/1 + 2006/2 + 2005/3 +... +2/2006 + 1/2007
Tính B/A
chịuiuiuiuiuiuiuiuiuiuiuiu
A=20008+2007/2+2006/3+2005/4+...+2/2007+1/2008 / 1/2+1/3+1/4+1/5+1/6+1/7+...+1/2008
a=...
tính M :N biết: N=1/2+1/3+1/4+......+1/2007+1/2008 và M= 2007/1+2006/2+2005/3+......+2/2006+1/2007
\(\frac{M}{N}=\frac{\frac{1}{2007}+\frac{2}{2006}+......+\frac{2006}{2}+\frac{2007}{1}}{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+.......+\frac{1}{2006}+\frac{1}{2007}}\)
\(\frac{M}{N}=\frac{\frac{1}{2007}+1+\frac{2}{2006}+1+.......+\frac{2007}{1}+1+\frac{2008}{2008}-2008}{\frac{1}{2008}+\frac{1}{2007}+\frac{1}{2006}+.....+\frac{1}{2}}\)
\(\frac{M}{N}=\frac{\frac{2008}{2007}+\frac{2008}{2006}+....+\frac{2008}{1}+\frac{2008}{2008}-2008}{\frac{1}{2008}+........+\frac{1}{2}}\)
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A=2008+2007/2+2006/3+2005/4+......+2/2007+1/2008 tất cả trên 1/2+1/3+1/4+1/5+......+1/2008+1/2009
\(B=2008+\frac{2007}{2}+\frac{2006}{3}+\frac{2005}{4}+...+\frac{2}{2007}+\frac{1}{2008}\)
\(=1+1+\frac{2007}{2}+1+\frac{2006}{3}+...+1+\frac{1}{2008}\)
\(=\frac{2009}{2009}+\frac{2009}{2}+\frac{2009}{3}+...+\frac{2009}{2008}\)
\(=2009\left(\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2008}+\frac{1}{2009}\right)\)
Suy ra \(A=2009\).
tính nhanh
A=2008+2007/2+2006/3+2005/4+…..+2/2007+1/2008
1/2+1/3+1/4+1/5+…..+1/2007+1/2008
A=2008+2007/2+2006/3+2005/4+...+2/2007+1/2008
1/2+1/3+1/4+1/5+...+1/2007+1/2008
=(1+2007/2)+(1+2006/3)+(1+2005/4)+...+(1+2/2007)+(1+1/2008)
1/2+1/3+1/4+...+1/2008
=2009(1/2+1/3+1/4+...+1/2008)
1/2+1/3+1/4+..+1/2008
=2009