A - B =(1 + 1/3 + 1/5 + 1/7 + ... + 1/2009 +1/2011) - (1/2 + 1/4 + 1/6 + ... + 1/2010 + 1/2012 )
A - B = 1 + 1/3 + 1/5 + 1/7 + ... + 1/2009 +1/2011 - 1/2- 1/4 - 1/6 - ... - 1/2010 1/2012
A - B = 1 - 1/2 + 1/3 - 1/4 + 1/5 - 1/6 +..... 1/2011 - 1/2012
A - B = 1/ 1.2 + 1/3.4 + 1/5.6 + .... + 1/2011. 2012
A - B = 1 - 1 / 2012 = 2011 /2012 < 1
Vậy A - B < 1
So sánh A và B biết : a, A=-2 /2011 -3/112 -5/113 - 7/114 ; B=-1/2011 -7/112 -5/113 - 3/114
b, A= 2006/2007 - 2007/2008 + 2008 / 2009 -2009/2010 B=1/2006.2007 -1/2008.2009
Tính:
A=\(\frac{7}{3}\).\(\frac{11}{16}\)+\(\frac{10}{3}\).\(\frac{7}{16}\)-\(\frac{7}{6}\).\(\frac{5}{8}\)
B=1+2-3-4+5+6-7-8+.....+2005+2006-2007-2008+2009+2010
C=(1-\(\frac{1}{4}\))(1-\(\frac{1}{9}\))(1-\(\frac{1}{16}\))......(1-\(\frac{1}{100000}\))
D=\(\frac{17\frac{3}{4}.\frac{17}{5}+3\frac{2}{5}.82\frac{1}{4}}{2.34-3.17}\)
E=\(\frac{\frac{2008}{2011}+\frac{2009}{2010}+\frac{2010}{2009}+\frac{2011}{2008}+\frac{2012}{503}}{\frac{1}{2011}+\frac{1}{2010}+\frac{1}{2009}+\frac{1}{2008}}\)
F=(2-\(\frac{2}{1.3}\))+(2-\(\frac{2}{3.5}\))+(2-\(\frac{2}{5.7}\))+.....+(2-\(\frac{2}{2009.2011}\))
Tính:
P = (1/2 +1/3 + 1/4 + .......+1/2012)/ (2011/1 +2010/2 +2009/3 +........+1/2011)
tìm x biết :
a)(x+4) / 2010 + (x+3)/2011 =( x+2)/2012 + (x+1)/2013
b) (x-1)/2010 + (x-2)/2009 = (x-3)/2008 + (x-4)/2007
P=\(\dfrac{\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{4}+...+\dfrac{1}{2012}}{\dfrac{2011}{1}+\dfrac{2010}{2}+\dfrac{2009}{3}+...+\dfrac{1}{2011}}\)
Cho A= \(\frac{1}{2}+\frac{1}{3}+...+\frac{1}{2011}\)
B= \(\frac{2011}{1}+\frac{2010}{2}+\frac{2009}{3}+...+\frac{2}{2010}+\frac{1}{2011}\)
Tính \(\frac{B}{A}\)
1)thực hiện phép tính hợp lí nhất có thể:
\(D=\left(\frac{1}{2}+\frac{1}{3}+\frac{1}{4}+...+\frac{1}{2012}\right):\left(\frac{2011}{1}+\frac{2010}{2}+\frac{2009}{3}+...+\frac{1}{2011}\right)\)
a, |2x\(^2\)+1|+5(x+y-z)\(^{2010}\) \(\le\)1
b, |x-2009|+|x-2010|+|y-2011|+|x-2012|=3
c, |2x-3|+|x\(^2\)+2|= x\(^2\)-2x+5
d, 3<|x-2|\(\le\)6
Cho A= 1 + \(\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{4}+...+\dfrac{1}{4034}\); B = 1 + \(\dfrac{1}{3}+\dfrac{1}{5}+\dfrac{1}{7}+...+\dfrac{1}{4033}\)
So sánh \(\dfrac{A}{B}\)với 1\(\dfrac{2017}{2018}\)