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 \(A=\dfrac{-4949}{19800}\)

= 60 bn nhé

3.4.5=60

k nha

3x4x5=60

Đặt A = 1 x 2 x 3 + 2 x 3 x 4 + 3 x 4 x 5 +....+ 98 x 99 x 100

4A = 1 x 2 x 3 x 4 + 2 x 3 x 4 x 4 + 4 x 5 x 4 +....+ 98 x 99 x 100 x 4

4A = 1 x 2 x 3 x ( 4 - 0 ) + 2 x 3 x 4 x ( 5 - 1 ) + 4 x 5 x 6 x ( 7 - 3 ) +....+ 98 x 99 x 100 x ( 101 - 97 )

4A = 1 x 2 x 3 x 4 + 2 x 3 x 4 x 5 - 1 x 2 x 3 x 4 + 4 x 5 x 6 x 7 - 3 x 4 x 5 x 6 + .... + 98 x 99 x 100 x 101 - 98 x 99 x 100 x 97

A = 98 x 99 x 100 x 97 / 4

A = 98 x 99 x 25 x 97

\(\frac{1}{2\cdot3\cdot4}+\frac{1}{3\cdot4\cdot5}+....+\frac{1}{39\cdot40\cdot41}\)

Đặt \(A=\frac{1}{2\cdot3\cdot4}+\frac{1}{3\cdot4\cdot5}+...+\frac{1}{39\cdot40\cdot41}\)

\(A=\frac{4-2}{2\cdot3\cdot4}+\frac{5-3}{3\cdot4\cdot5}+....+\frac{41-39}{39\cdot40\cdot41}\)

\(A=\frac{2}{2\cdot3}+\frac{2}{3\cdot4}+\frac{2}{4\cdot5}+...+\frac{2}{39\cdot40}+\frac{2}{40\cdot41}\)

\(A=\frac{1}{2}\cdot\left(\frac{1}{1\cdot2}-\frac{1}{3\cdot4}+\frac{1}{3\cdot4}-\frac{1}{4\cdot5}+....+\frac{1}{39\cdot40}-\frac{1}{40\cdot41}\right)\)

\(A=\frac{1}{2}\cdot\left(\frac{1}{1\cdot2}-\frac{1}{40\cdot41}\right)\)

\(A=\frac{1}{2}\cdot\frac{819}{1640}\)

\(A=\frac{819}{3280}\)