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化简:1/2!+2/3!+3/4!+...+(n-1)/n!(n属于N*,n>=2)
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化简:1/2!+2/3!+3/4!+...+(n-1)/n!(n属于N*,n>=2)
▼优质解答
答案和解析
(n-1)/n!
=n/n!-1/n!
=1/(n-1)!-1/n!
所以1/2!+2/3!+3/4!+...+(n-1)/n!
=(1/1!-1/2!)+(1/2!-1/3!)+……+[1/(n-1)!-1/n!]
=1/1!-1/n!
=1-1/n!
=n/n!-1/n!
=1/(n-1)!-1/n!
所以1/2!+2/3!+3/4!+...+(n-1)/n!
=(1/1!-1/2!)+(1/2!-1/3!)+……+[1/(n-1)!-1/n!]
=1/1!-1/n!
=1-1/n!
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