09Nov

# Find a closed form for Sn = 1 *1!+2*2!+...+n*n! for integer n>=1 Your response should have a factorial.

romojose2
Mathematics
1 1

Find a closed form for Sn = 1 *1!+2*2!+...+n*n! for integer n>=1 Your response should have a factorial.

09Nov

romojose2
Mathematics
1 1

Hello, [latex] x_{1} =1*1!=1\ x_{2} =2*2!=4\ x_{3} =3*3!=18\ x_{4} =4*4!=96\ S_{1} = x_{1}=1=2!-1\ S_{2} = x_{1}+x_{2}=1+4=5=3!-1\ S_{3} = x_{1}+x_{2}+x_{3}=5+18=23=4!-1\ S_{4} = x_{1}+x_{2}+x_{3}+x_{4}=23+96=119=5!-1\ oxed{S_{n} = (n+1)!-1}\ [/latex]