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Find the sum of the series (sum(r=1)^(n)...

Find the sum of the series `(sum_(r=1)^(n) rxxr !)`

Text Solution

Verified by Experts

Here, the general term of the series is
`T_(r )=r xxr! = (r+1-r)r!`
=(r+1)r!-r!
=(r+1)!-r!
Hence, `T_(1)=2!-1!`
`T_(2)=3!-2!`
`T_(3)=4!-3!`
`T_(n)=(n+1)!-n!`
Adding all the above terms, we have the sum of n terms, i.e.
`S_(n)=(n+1)!=1`
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