作业帮1/2!+2/3!+3/4!+.+n/(n+1)!求和
来源：学生作业帮 编辑：作业帮 分类：综合作业 时间：2024/05/16 17:57:39
1/2!+2/3!+3/4!+.+n/(n+1)!求和
1/2!+2/3!+3/4!+.+n/(n+1)!
=1/2!+2/3!+3/4!+.+n/(n+1)!+1/(n+1)!-1/(n+1)!
=1/2!+2/3!+3/4!+.+1/n!-1/(n+1)!
=1-1/(n+1)!
再问： 详细点，我看不懂1/2!+2/3!+3/4!+.....+1/n!=1不懂
再答： 1/2!+2/3!+3/4!+.....+(n-1)/n!+n/(n+1)! =1/2!+2/3!+3/4!+.....+(n-1)/n!+n/(n+1)!+1/(n+1)!-1/(n+1)! =1/2!+2/3!+3/4!+.....+(n-1)/n!+(n+1)/(n+1)!-1/(n+1)! =1/2!+2/3!+3/4!+.....+(n-1)/n!+1/n!-1/(n+1)! =1-1/(n+1)! 从后往前消项,明白了吧
再问： 明白
=1/2!+2/3!+3/4!+.+n/(n+1)!+1/(n+1)!-1/(n+1)!
=1/2!+2/3!+3/4!+.+1/n!-1/(n+1)!
=1-1/(n+1)!
再问： 详细点，我看不懂1/2!+2/3!+3/4!+.....+1/n!=1不懂
再答： 1/2!+2/3!+3/4!+.....+(n-1)/n!+n/(n+1)! =1/2!+2/3!+3/4!+.....+(n-1)/n!+n/(n+1)!+1/(n+1)!-1/(n+1)! =1/2!+2/3!+3/4!+.....+(n-1)/n!+(n+1)/(n+1)!-1/(n+1)! =1/2!+2/3!+3/4!+.....+(n-1)/n!+1/n!-1/(n+1)! =1-1/(n+1)! 从后往前消项,明白了吧
再问： 明白
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