B= 1.2+2.3+3.4+...+2009.2010

=>3B=1.2.3+2.3.3+3.4.3+...+2009.2010.3

=1.2.(3-0)+2.3.(4-1)+3.4.(5-2)+...+2009.2010.(2011-2008)

=1.2.3-0.1.2+2.3.4-1.2.3+3.4.5-2.3.4+....+2009.2010.2011-2008.2009.2010

=2009.2010.2011

=>B=\(\frac{2009.2010.2011}{3}=2706866330\)

ta có: 1x2+2x3+3x4+....+n(n+1) 
=1x(1+1)+2x(2+1)+3x(3+1)+....­n(n+1) 
=(1^2+2^2+3^2+¡­+n^2)+(1+2+3+....+n) 
=n(n+1)(2n+1)/6+n(n+1)/2 
=[n(n+1)[(2n+1)+3]/6

thay n=2009=> B=\(\frac{2009.\left(2009+1\right).\left(2009.2+1\right)+3}{6}\)=2704847286

\(\dfrac{1}{1\times2}+\dfrac{1}{2\times3}+\dfrac{1}{3\times4}+....+\dfrac{1}{24\times25}\)

\(=1-\dfrac{1}{2}+\dfrac{1}{2}-\dfrac{1}{3}+...+\dfrac{1}{24}-\dfrac{1}{25}\)

\(=1-\dfrac{1}{25}\)

\(=\dfrac{24}{25}\)

Nhanh giúp mình với cả nhà ơi

\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{2010}-\frac{1}{2011}\)

\(=1-\frac{1}{2011}\)

\(=\frac{2010}{2011}\)

=1/1-1/2+1/2-1/3+1/3-1/4+...+1/2010-1/2011

= 1 - 1/2011

= 2010/ 2011

Đáp số: 2010/2011

Chúy ý công thức: \(\frac{1}{n\left(n+1\right)}=\frac{1}{n}-\frac{1}{n+1}\)

= 1/1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + ... + 1/2010 - 1/2011

= 1 - 1/2011

= 2010/2011

Đáp sô: 2010/2011

Chú ý công thưc:              \(\frac{1}{n\left(n+1\right)}=\frac{1}{n}-\frac{1}{n+1}\)

S=1-\(\frac{1}{2}\)+\(\frac{1}{2}\)-\(\frac{1}{3}\)+...+\(\frac{1}{2009}\)-\(\frac{1}{2010}\)

S=1-\(\frac{1}{2010}\)

S=\(\frac{2009}{2010}\)

k nha bn

\(S=\frac{1}{1\times2}+\frac{1}{2\times3}+\frac{1}{3\times4}+...+\frac{1}{2008\times2009}+\frac{1}{2009\times2010}\)

\(=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{2008}-\frac{1}{2009}+\frac{1}{2009}-\frac{1}{2010}\)

\(=1-\frac{1}{2010}\)

\(=\frac{2009}{2010}\)

Vậy \(S=\frac{2009}{2010}\)

Học tốt #

s = 1- 1/2+ 1/2- 1/3+ 1/3- 1/4 ......-1/2008- 1/2009+ 1/2009- 1/2010

s =1- 1/2010

s = 2009/2010

ai làm nhanh mik cho

mik cho

haizzz đáng tiếc tôi muốn ns là:  ko bao f và đừng mong chờ OK

ai làm dc mik cho

Đéo hiểu 

ai trả lời dc mik cho

ai giai ho mik đi'=))

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