Mathematics, 08.08.2019 02:10 gabriellabadon2
If 5 t n2, then 5t m (5 points) (5 points) 5. 1(11) +2(2! )+++ for all n e i
Answers: 3
![S_{n}=1*1!+2*2!+3*3!+4*4!+...........+n*n!\\\\T_{n}{\text{general term}}=n*n!\\\\ \sum _{k=1}^{k=n}t_{k}\\\\\sum _{k=1}^{k=n}k(k!)\\\\\sum _{k=1}^{k=n}(k+1-1)(k!)\\\\\sum _{k=1}^{k=n}[(k+1)!-k!]\\\\=(1!+2!+3!+.............(n+1)!)-(1!+2!+3!+..........+n!)\\\\=(n+1)!\\\\----{\text{Cancelling out like terms}}](/tpl/images/0173/0443/c0656.png)
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If 5 t n2, then 5t m (5 points) (5 points) 5. 1(11) +2(2! )+++ for all n e i...
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