B = 2 - 4 - 6 + 8 + 10 - 12 -14 + 16 + ...+ 2010 - 2012 - 2014 + 2016

   = (2 - 4 - 6 + 8 ) + ( 10 - 12 -14 +16 ) + ...+ ( 2010 - 2012 - 2014 + 2016 )

   = 0 + 0 +...+ 0 + 0 (có 252 số hạng 0)

    = 0

Ta có:  Từ 2 đến 2016 có \(\frac{2016-2}{2}+1=1008\)

B=(2-4)-(6-8)+(10-12)-(14-16)+...+(2010-2012)-(2014-2016)  như vậy có 1008:2=504 nhóm

=-2+2-2+2+...-2+2 có 504 số hạng trong đó có: 525 số -2 và 525 số +2

=0

\(C=\frac{1}{1.2.3}+\frac{1}{2.3.4}+\frac{1}{3.4.5}+...+\frac{1}{9.10.11}\)

\(\Rightarrow2.C=\frac{2}{1.2.3}+\frac{2}{2.3.4}+\frac{2}{3.4.5}+...+\frac{2}{9.10.11}=\frac{1}{2}\left(\frac{2}{1.3}\right)+\frac{1}{3}\left(\frac{2}{2.4}\right)+\frac{1}{4}\left(\frac{2}{3.5}\right)+\)\(...+\frac{1}{10}\left(\frac{2}{9.11}\right)\)

\(=\frac{1}{2}\left(1-\frac{1}{3}\right)+\frac{1}{3}\left(\frac{1}{2}-\frac{1}{4}\right)+\frac{1}{4}\left(\frac{1}{3}-\frac{1}{5}\right)+...+\frac{1}{10}\left(\frac{1}{9}-\frac{1}{11}\right)\)

\(=\frac{1}{2}-\frac{1}{2.3}+\frac{1}{3.2}-\frac{1}{3.4}+\frac{1}{4.3}-\frac{1}{4.5}+...+\frac{1}{10.9}-\frac{1}{10.11}\)

\(=\frac{1}{2}-\frac{1}{10.11}=\frac{27}{55}\)

=> C=27/110

B=1/1.2.3 +1/2.3.4 +1/3.4.5 +.....+1/9.10.11  

=1/2.(2/1.2.3 +2/2.3.4 +2/3.4.5 +.......+2/9.10.11)  

=1/2.(1/1.2 -1/2.3 +1/2.3 -1/3.4 +1/4.5 +........+1/9.10 -1/10 .11)  

=1/2 .(1/1.2 -1/10.11)  

= 1/2 .27/55  

=27/110

tìm thừa số chung cùng số cuối rồi sẽ tính ra

cau hoi nay hay qua

có ai giúp tôi ko

Ta có:\(B=\dfrac{1}{6}+\dfrac{1}{24}+\dfrac{1}{60}+...+\dfrac{1}{990}\)

\(2B=\dfrac{2}{6}+\dfrac{2}{24}+\dfrac{2}{60}+...+\dfrac{2}{990}\)

\(2B=\dfrac{2}{1\cdot2\cdot3}+\dfrac{2}{2\cdot3\cdot4}+\dfrac{2}{3\cdot4\cdot5}+...+\dfrac{2}{9\cdot10\cdot11}\)

\(2B=\dfrac{1}{1\cdot2}-\dfrac{1}{2\cdot3}+\dfrac{1}{2\cdot3}-\dfrac{1}{3\cdot4}+\dfrac{1}{3\cdot4}-\dfrac{1}{4\cdot5}+...+\dfrac{1}{9\cdot10}-\dfrac{1}{10\cdot11}\)

\(2B=\dfrac{1}{1\cdot2}-\dfrac{1}{10\cdot11}\)

\(2B=\dfrac{27}{55}\)

\(B=\dfrac{27}{55}:2\)

\(B=\dfrac{27}{110}\)