Đặt \(A=\dfrac{1}{1\cdot2\cdot3}+\dfrac{1}{2\cdot3\cdot4}+\dfrac{1}{3\cdot4\cdot5}+...+\dfrac{1}{98\cdot99\cdot100}\)

Ta có: \(A=\dfrac{1}{1\cdot2\cdot3}+\dfrac{1}{2\cdot3\cdot4}+\dfrac{1}{3\cdot4\cdot5}+...+\dfrac{1}{98\cdot99\cdot100}\)

\(\Leftrightarrow2A=\dfrac{2}{1\cdot2\cdot3}+\dfrac{2}{2\cdot3\cdot4}+\dfrac{2}{3\cdot4\cdot5}+...+\dfrac{2}{98\cdot99\cdot100}\)

\(\Leftrightarrow2A=-\dfrac{1}{1\cdot2}+\dfrac{1}{2\cdot3}-\dfrac{1}{2\cdot3}+\dfrac{1}{3\cdot4}-\dfrac{1}{3\cdot4}+\dfrac{1}{4\cdot5}-\dfrac{1}{4\cdot5}+...-\dfrac{1}{98\cdot99}+\dfrac{1}{99\cdot100}\)

\(\Leftrightarrow2A=-\dfrac{1}{2}+\dfrac{1}{99\cdot100}\)

\(\Leftrightarrow2A=\dfrac{-1}{2}+\dfrac{1}{9900}\)

\(\Leftrightarrow2A=\dfrac{-4950}{9900}+\dfrac{1}{9900}=\dfrac{-4949}{9900}\)

hay \(A=\dfrac{-4949}{19800}\)

1x2x3=6 chọn đúng nha

\(1.2.3=2.3=6\)

1 x 2 x 3 = 6 nha bạn !

chúc bạn học tốt nhé !

hihi

k di minh tra loi

Gọi A = 1.2.3 + 2.3.4 + ................... + 2011.2012.2013

4A = 1.2.3.4 + 2.3.4.4 + ...................... + 2011.2012.2013.4

4A = 1.2.3.4 + 2.3.4.(5 - 1) +..................... + 2011.2012.2013.(2014 - 2010)

4A = 1.2.3.4 + 2.3.4.5 - 1.2.3.4 + .................... + 2011.2012.2013.2014 - 2010.2011.2012.2013

4A = 2011.2012.2013.2014

A = \(\frac{2011.2012.2013.2014}{4}=2011.503.2013.2014=..........\)

4xA=1x2x3x4+2x3x4x4+3x4x5x4+...+15x16x17x4

4xA=1x2x3x4+2x3x4x(5-1)+3x4x5x(6-2)+...+-15x16x17x(18-14)

4xA=1x2x3x4-1x2x3x4+2x3x4x5-2x3x4x5+3x4x5x6-...-14x15x16x17+15x16x17x18=15x16x17x18

=> A=15x4x17x18=18360