Question

Tính B= 1.2.3 + 2.3.4 + 3.4.5 +....+ (n-1)n(n+1)

Answer 1

=\(\frac{\left(n-1\right)n\left(n+1\right)\left(n+2\right)}{4}\)

Answer 2

4B = 1.2.3.4 + 2.3.4.4 + ... + (n-1)n(n+1).4

= 1.2.3.4 - 0.1.2.3 + 2.3.4.5 - 1.2.3.4 + ... + (n-1)n(n+1)(n+2) - [(n-2)(n-1)n(n+1)]

= (n-1)n(n+1)(n+2) - 0.1.2.3

= (n-1)n(n+1)(n+2)

suy ra \(B = {(n-1)n(n+1)(n+2)\over 4}\)