设Sn=1/2+1/6+1/12+•••+ 1/〔n(n+1)〕,且SnSn+1 =3/4,则n的值为()

问题描述:

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