设S=1/2+1/6+1/12+...+1/n(n+1),且Sn*S(n+1)=3/4,则n的值为
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解决时间 2021-02-13 13:54
- 提问者网友:西路不相离
- 2021-02-13 10:17
设S=1/2+1/6+1/12+...+1/n(n+1),且Sn*S(n+1)=3/4,则n的值为
最佳答案
- 二级知识专家网友:啵啵桃汀
- 2021-02-13 11:48
1/n(n+1)=1/n -1/(n+1),
Sn=1/2+1/6+1/12+...+1/n(n+1)
=1-1/2+1/2-1/3+...+1/n -1/(n+1)
=1-1/(n+1)
=n/(n+1)
S(n+1)=(n+1)/(n+2)
Sn*S(n+1)
=n/(n+1) * (n+1)/(n+2)
=n/(n+2)=3/4
3n+6=4n
n=6
Sn=1/2+1/6+1/12+...+1/n(n+1)
=1-1/2+1/2-1/3+...+1/n -1/(n+1)
=1-1/(n+1)
=n/(n+1)
S(n+1)=(n+1)/(n+2)
Sn*S(n+1)
=n/(n+1) * (n+1)/(n+2)
=n/(n+2)=3/4
3n+6=4n
n=6
全部回答
- 1楼网友:伤口狠精致
- 2021-02-13 12:01
sn=1/2+1/6+1/12+……+1/n(n+1)
=1/2+(1/2-1/3)+(1/3-1/4)+……+(1/n-1/n+1)
=1-1/n+1=n/n+1
sn+1=n+1/n+2
sn x sn+1=n/n+1 * n+1/n+2=n/n+2=3/4 n=6
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