Question

[nguyen thi phuong anh]

tính S=0.2+2.4+4.6+...............+2n(2n+2)

Answer 1

[Đoàn Đức Hà]

\(S=0.2+2.4+4.6+...+2n\left(2n+2\right)\)

\(6S=2.4.6+4.6.\left(8-2\right)+...+2n\left(2n+2\right)\left[\left(2n+4\right)-\left(2n-2\right)\right]\)

\(=2.4.6+4.6.8-2.4.6+...+2n\left(2n+2\right)\left(2n+4\right)-\left(2n-2\right).2n.\left(2n+2\right)\)

\(=2n\left(2n+2\right)\left(2n+4\right)\)

Suy ra \(S=\frac{2n\left(2n+2\right)\left(2n+4\right)}{6}\)