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](/uploads/image/z/8645900-68-0.jpg?t=%E8%AE%BES%3D1%2F2%2B1%2F6%2B1%2F12%2B...%2B1%2Fn%28n%2B1%29%2C%E4%B8%94Sn%2AS%28n%2B1%29%3D3%2F4%2C%E5%88%99n%E7%9A%84%E5%80%BC%E4%B8%BA)
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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