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Prof-that-n-1-10-n-n-11-1-

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Question Number 155842 by zainaltanjung last updated on 05/Oct/21
Prof that: Σ_(n=1) ^(10) n.n!=11!−1
Profthat:∑10n=1n.n!=11!−1
Commented by puissant last updated on 05/Oct/21
Q155803
Q155803
Answered by mr W last updated on 05/Oct/21
Σ_(n=1) ^k n×n! =Σ_(n=1) ^k [(n+1)×n!−n!] =Σ_(n=1) ^k [(n+1)!−n!] =(k+1)!−1! =(k+1)!−1
∑kn=1n×n!=∑kn=1[(n+1)×n!−n!]=∑kn=1[(n+1)!−n!]=(k+1)!−1!=(k+1)!−1

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