设Sn=1/2+1/6+1/12+•••+ 1/〔n(n+1)〕,且SnSn+1 =3/4,则n的值为( )
来源:学生作业帮助网 编辑:作业帮 时间:2024/07/04 05:12:00
![设Sn=1/2+1/6+1/12+•••+ 1/〔n(n+1)〕,且SnSn+1 =3/4,则n的值为( )](/uploads/image/z/10213825-49-5.jpg?t=%E8%AE%BESn%3D1%2F2%2B1%2F6%2B1%2F12%2B%26%238226%3B%26%238226%3B%26%238226%3B%2B+1%2F%E3%80%94n%28n%2B1%29%E3%80%95%2C%E4%B8%94SnSn%2B1+%EF%BC%9D3%2F4%2C%E5%88%99n%E7%9A%84%E5%80%BC%E4%B8%BA%EF%BC%88++%EF%BC%89)
设Sn=1/2+1/6+1/12+•••+ 1/〔n(n+1)〕,且SnSn+1 =3/4,则n的值为( )
设Sn=1/2+1/6+1/12+•••+ 1/〔n(n+1)〕,且SnSn+1 =3/4,则n的值为( )
设Sn=1/2+1/6+1/12+•••+ 1/〔n(n+1)〕,且SnSn+1 =3/4,则n的值为( )
Sn=1-1/2+1/2-1/3+1/3-1/4+……+1/n-1/(n+1)
=1-1/(n+1)
=n/(n+1)
所以Sn*S(n+1)=[n/(n+1)][(n+1)/(n+2)]=n/(n+2)=3/4=6/8
所以n=6