Επειδή nxn! = (n+1-1)xn! = (n+1)xn! - n! = (n+1)! - n!θα είναι:1x1! + 2x2! + ... + nxn! = (2! - 1!) + (3! - 2!) + ... + ((n+1)! - n!) = (n+1)! - 1! = (n+1)! - 1
Επειδή
ΑπάντησηΔιαγραφήnxn! = (n+1-1)xn! = (n+1)xn! - n! = (n+1)! - n!
θα είναι:
1x1! + 2x2! + ... + nxn! =
(2! - 1!) + (3! - 2!) + ... + ((n+1)! - n!) = (n+1)! - 1! =
(n+1)! - 1