What is the value of 1×1!+2×2!+3!×3!+............n×n!;where n! means n factorial or n(n−1)(n−2)...1  Pick one:
A) n(n−1)(n−1)!  B) n(n−1)(n−1)!  C) n(n−1)(n−1)!  D) (n+1)!−1!  E) None of these
Explanation :   1×1!=(2−1)×1!=2×1!−1×1!=2!−1!2×2!=(3−1)×2!=3×2!−2!=3!−2!3×3!=(4−1)×3!=4×3!−3!=4!−3!......n×n!=(n+1−1)×n!=(n+1)(n!)−n!=(n+1)!−n!Summing up all these terms, we get (n+1)! - 1!   Answer : (n+1)!−1!
<result>D</result>
What is the value of 1×1!+2×2!+3!×3!+............n×n!;where n! means n factorial or n(n−1)(n−2)...1