Question

1+1*2+2*3+3...........*39+39*40+40

S=

giúp mik vs các bn ơi mik đang cần gấp ak

Answer 1

ta có: \(S=1+1\times2+2\times3+3\times4+...+38\times39+39\times40+40\)

\(\Rightarrow3S=1\times3+1\times2\times3+2\times3\times3+...+39\times40\times3+40\times3\)

\(3S=3+1\times2\times\left(3-0\right)+2\times3\times\left(4-1\right)+...+39\times40\times\left(41-38\right)+120\)

\(3S=3+1\times2\times3+2\times3\times4-1\times2\times3+...+39\times40\times41-38\times39\times40+120\)

\(3S=\left(3+1.2.3+...+39.40.41+120\right)-\left(1.2.3+...+38.38.40\right)\)

\(3S=3+39.40.41+120\)

\(\Rightarrow S=\left(3+39.40.41+120\right):3\)

\(S=21361\)