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