设Sn=1/2+1/6+1/12+…+1/n（n+1）,且Sn*Sn+1=3/4,则n=多少?
问题描述：
设Sn=1/2+1/6+1/12+…+1/n（n+1）,且Sn*Sn+1=3/4,则n=多少?
答
Sn=1/2+1/6+1/12+…+1/n（n+1）=1/(1*2)+1/(2*3)+...+1/(n)*(n+1)=1-1/2+1/2-1/3+...+1/n-1/(n+1)=1-1/(n+1)=n/(n+1)所以Sn+1=1-1/(n+2)=(n+1)/(n+2)sn*sn+1=3/4n/(n+1)*(n+1)/(n+2)=3/4n/(n+2)=3/44n=3n+6n=6