数列求和sn=(x+1/x)^2+(x^2+1/x^2)^2+……(x^n+1/x^n)^2
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![数列求和sn=(x+1/x)^2+(x^2+1/x^2)^2+……(x^n+1/x^n)^2](/uploads/image/z/645529-49-9.jpg?t=%E6%95%B0%E5%88%97%E6%B1%82%E5%92%8Csn%3D%28x%2B1%2Fx%29%5E2%2B%28x%5E2%2B1%2Fx%5E2%29%5E2%2B%E2%80%A6%E2%80%A6%EF%BC%88x%5En%2B1%2Fx%5En%29%5E2)
数列求和sn=(x+1/x)^2+(x^2+1/x^2)^2+……(x^n+1/x^n)^2
数列求和sn=(x+1/x)^2+(x^2+1/x^2)^2+……(x^n+1/x^n)^2
数列求和sn=(x+1/x)^2+(x^2+1/x^2)^2+……(x^n+1/x^n)^2
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