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为什么是=(x^2 +2(x+1/x)^2 =x^2 + 2*x*1/x +(1/x)^2 =x^2 +2 +1/x^2