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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设S=1/2+1/6+1/12+...+1/n(n+1),且Sn*S(n+1)=3/4,则n的值为
设S=1/2+1/6+1/12+...+1/n(n+1),且Sn*S(n+1)=3/4,则n的值为

设S=1/2+1/6+1/12+...+1/n(n+1),且Sn*S(n+1)=3/4,则n的值为
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