Sn=1/2+1/6+1/12+...+1/[n(n+1)]且Sn*Sn+1=3/4则n=?希望有大致过程,

Question

Sn= 1/2 + 1/6 + 1/12 +...+ 1/[n(n+1)]
且 Sn * Sn+1 = 3/4
则n=?
希望有大致过程,

Answer 1

1/n(n+1)=1/n-1/(n+1)
所以 Sn1-1/2+1/2-1/3+1/3-1/4+……+1/n-1/(n+1)=1-1/(n+1)=n/(n+1)
所以 S(n+1)=(n+1)/(n+2)
所以[n/(n+1)][(n+1)/(n+2)]=3/4
n/(n+2)=3/4
n=6