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heureka

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 #2
avatar+26396 
+5

Find a closed form for

S_n=1*1!+2*2!+...+n*n!.

for integers n>=1.

Your response should have a factorial.

 

Example for n=4:

S4=11!+22!+33!+44!|4!=3!4S4=11!+22!+33!+43!4S4=11!+22!+3!(3+44)S4=11!+22!+3!(3+42)|3!=2!3S4=11!+22!+2!3(3+42)S4=11!+2![ 2+3(3+42) ]|2!=1!2S4=11!+1!2[ 2+3(3+42) ]S4=1!{ 1+2[ 2+3(3+42) ] }|1!=1S4=1{ 1+2[ 2+3(3+42=41+42=4(4+1)1=451) ] }S4=1{ 1+2[ 2+3(451) ] }S4=1[ 1+2( 2+3453 ) ]S4=1[ 1+2( 3451 ) ]S4=1( 1+23452 )S4=1( 23451 )S4=123451S4=5!111!+22!+33!+44!=5!1

 

Sn=11!+22!+...+nn!Sn=(n+1)!1

 

laugh

.
10.08.2016
 #1
avatar+26396 
+5

Kmax= (6.63*10-34J*s) (7.09*1014s) - 2.17*10-19J

Im not sure if the 1014s is suppose to be 1014s-1 or not.

Someone told me it should but it doesnt say on the problem. 

 

Kmax=(6.631034Js)(7.091014s1)2.171019JKmax=6.637.0910341014Jss12.171019JKmax=6.637.091034+14Jss12.171019JKmax=6.637.091020Js1s12.171019JKmax=6.637.091020Js112.171019JKmax=6.637.091020Js02.171019J|s0=1Kmax=6.637.091020J12.171019JKmax=47.00671020J2.171019JKmax=4.70067101020J2.171019JKmax=4.7006710120J2.171019JKmax=4.700671019 J2.171019 JKmax=(4.700672.17)1019 JKmax=2.530671019 J

 

laugh

10.08.2016