Question

Tính:

Answer 1

\(S=1\cdot2+2\cdot3+3\cdot4+...+39\cdot40\)

\(3S=1\cdot2\cdot3+2\cdot3\cdot\left(4-1\right)+3\cdot4\cdot\left(5-2\right)+...+39\cdot40\cdot\left(41-38\right)\)

\(3S=1\cdot2\cdot3+2\cdot3\cdot4-1\cdot2\cdot3+...+39\cdot40\cdot41-38\cdot39\cdot40\)

\(3S=39\cdot40\cdot41\)\(\Rightarrow S=\dfrac{39\cdot40\cdot41}{3}=21320\)

Answer 2

Ta có : \(S=1.2+2.3+3.4+...+38.39+39.40\)

\(3S=1.2.3+2.3.3+3.4.3+...+38.39.3+39.40.3\)

\(3S=1.2.3+2.3.\left(4-1\right)+3.4.\left(5-2\right)+...+39.40.\left(41-38\right)\) \(3S=39.40.41\)

\(S=\dfrac{39.40.41}{3}\)\(=21320\)