x→∞,(1/2!+2/3!+…+n/(n+1)!)等于多少?

题目详情

▼优质解答

答案和解析

因为n/(n+1)!=1/n!-1/(n+1)!
所以,1/2!+2/3!+…+n/(n+1)!=1/1!-1/2!+1/2!-1/3!+1/3!-1/4!+...+1/n!-1/(n+1)!=1-1/(n+1)!
故n→∞时,(1/2!+2/3!+…+n/(n+1)!)=1

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