(4-x).(2x+1/3)=(2006/2007-2007/2008+2008/2009).(2/3-1/4-5/12)
giúp mình nhé thank nhiều :D
Tính : 1+2-3-4+5+6-7-8+9+10-11-12+......+2006-2007-2008+2009
Các bạn ghi cách giải cho mình nhé cảm ơn nhiều lắm!
Ta có : 1 + 2 - 3 - 4 + 5 + 6 - 7 - 8 + 9 + 10 - 11 - 12+......+ 2006 - 2007 - 2008 + 2009
= (1 + 2 - 3 - 4) + (5 + 6 - 7 - 8) + (9 + 10 - 11 - 12)+...... + (2005 + 2006 - 2007 - 2008) + 2009
= -4 + -4 + ...... + (-4) + 2009
= (-4) x 502 + 2009
= (-2008) + 2009
= 1
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
1. So sánh
a) A=1/2019 - 3/11^2 - 5/11^ - 7/11^4 và B= -1/2019 - 7/11^2 - 5/ 11^3 - 3/11^4
b) A= 2006/2007 - 2007/2008 + 2008/2009 - 2009/2010 và B= -1/2006 . 2007 - 1/2008 . 2009
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 \(A=2009\).
So sánh
bài 1 :A= 2006/2007-2007/2008+2008/2009-2009/2010
B= -1/2006*2007-1/2008*2009
bài 2: C= 2006/2007+2007/2008+2008/2009+2009/2006 với 4
Giải giúp mình câu này với các bạn ơi, mình cám ơn nhiều:
tính giá trị biểu thức:
\(y=\frac{2008+\frac{2007}{2}+\frac{2006}{3}+......+\frac{2}{2007}+\frac{1}{2008}}{\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+.....+\frac{1}{2008}+\frac{1}{2009}}\)
A =2008 + 2007/2 + 2006/3 + 2005/4 +.......+ 2/2007 + 1/2008
1/2 + 1/3 + 1/4 + 1/5 +....+ 1/2008 + 1/2009
(2008+2007/2+2006/3+2005/4+....+2/2007+1/2008) / (1/2+1/3+1/4+...+1/2009)
Xét tử
2008+2007/2+2006/3+2005/4+ ... +2/2007+1/2008
=(1+1+1+...+1)+2007/2+2006/3+2005/4+ ... +2/2007+1/2008
= 1+ (2007/2)+1+(2006/3)+1+(2005/4)+1+ ... + (2/2007)+1+(1/2008)+1
=2009/2009+2009/2+2009/3+2009/4+ ... + 2009/2007 + 2009/2008
=2009.(1/2+1/3+1/4+ ... + 1/2007+1/2008+1/2009)
Ta có tử số bằng: 2008+2007/2+2006/3+2005/4+…..+2/2007+1/2008
(Phân tích 2008 thành 2008 con số 1 rồi đưa vào các nhóm)
= (1 + 2007/2) + (1 + 2006/3) + (1 + 2005/4) +... + (1 + 2/2007) + ( 1 + 1/2008) + (1)
= 2009/2 + 2009/3 + 2009//4 + ……. + 2009/2007 + 2009/2008 + 2009/2009
= 2009 x (1/2 + 1/3 + 1/4 + ... + 1/2007 + 1/2008 + 1/2009)
Mẫu số: 1/2 + 1/3 + 1/4 + ... + 1/2007 + 1/2008 + 1/2009
Vậy A = 2009