当x=±1时,Sn=4n
当x≠±1时,
Sn=(x^2+2+1/x^2)+(1/x^4+2+1/x^4)+……+[x^(2n)+2+1/x^(2n)]
=[x^2+x^4+……+x^(2n)]+2n+[1/x^2+1/x^4+……+1/x^(2n)]
=[x^2-x^(2n+2)]/(1-x^2)+(1-1/x^(2n))/(x^2-1)+2n
=[x^(2n+2)-x^2+1]/(x^2-1)-1/[x^(2n)(x^2-1)]+2n
(x+1/x)^2=x^2+2*x*1/x+(1/x)^2=x^2+2+1/x^2