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Find the sum of firs 100 terms of the se...

Find the sum of firs 100 terms of the series whose general term is given by `T_(r)=(r^(2)+1)r!`.

Text Solution

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`T_(r)=(r^(2)+1)r!=(r(r+1)-(r-1))r!`
`=r(r+1)!-(r-1)r!`
`=V(r )-V(r-1)`, where V(r )=r(r+1)!
`sum_(r=1)^(100)T_(r)=sum_(r=1)^(100)[V(r )-V(r-1)]`
=V(100)-V(0)
`=100xx101!`-0
`=100xx101!`
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