\(\frac{1}{1\cdot2}+\frac{1}{2\cdot3}+\frac{1}{3\cdot4}+\frac{1}{4\cdot5}+...+\frac{1}{2009\cdot2010}\)

\(=\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+...+\frac{1}{2009}-\frac{1}{2010}\)

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

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

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

\(I=\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+.....+\frac{1}{2009.2010}\)

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

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

\(I=1-0-0-...-0-\frac{1}{2010}\)

\(I=1-\frac{1}{2010}=\frac{2009}{2010}\)

I = 1/1.2 + 1/2.3 + 1/3.4 + ... + 1/2009.2010

I = 1 - 1/2 + 1/2 - 1/3 + 1/3 - 1/4 + ... + 1/2009 - 1/2010

I = 1 - 1/2010

I = 2009/2010 

Vậy I = 2009/2010

I=1-1/2+1/2-1/3+1/3-1/4+...+1/2009-1/2010

I=1-1/2010

I=2009/2010

Vậy I=2009/2010

I = 1/1-1/2+1/2-1/3+1/3-1/4+...+1/2009-1/2010

I = 1-1/2010

I = 2009/2010

Chúc bạn học tốt nha

ta thấy: 1/1 - 1/2 = 1/2 = 1/1.2

            1/2 - 1/3 = 1/6 = 1/2.3

            1/3 - 1/4 = 1/12 = 1/3.4

tớ nêu cách làm rùi đó

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

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

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

1/1.2+1/2.3+...+1/2009.2010

=1-1/2+1/2-1/3+...+1/2009-1/2010

=1-1/2010

=2009/2010

=1 - 1/2 + 1/2 - 1/3 + ..... + 1/2009 - 1/2010

=1 - 1/2010

=2009/2010

1-1/2+1/2-1/3+1/3-1/4+... +1/2009-1/2010

1-1/2010=2009/2010

\(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{2009.2010}\)

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

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

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

M=1.2+2.3+3.4+...+2009.2010

3M = 1.2.3 + 2.3.3 + 3.4.3 + ... + 2009.2010.3

3M = 1.2.3 + 2.3.(4-1 ) + 3.4.(5-2) + ... + 2009.2010.(2011-2008)

3M = 1.2.3 + 2.3.4 - 1.2.3 +3.4.5 - 2.3.4 + ... + 2009.2010.2011 - 2008.2009.2010

3M = 2009.2010.2011

=> M = 2009.2010.2011 : 3

=> M = 2706866330

hí ae toi ms ngủ day

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

=1-1/2010

=-1/2009

lâu lằm k làm mấy bài kiểu nay... đúng k bạn ơi?????^-^

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

\(=1-\frac{1}{2010}=\frac{2009}{2010}\)

2009/2010