作业帮用公式求和：Sn=(x+1/x)^2+(x^2+1/x^2)^2+...(x^n+1/x^n)^2
来源：学生作业帮助网 编辑：作业帮 时间：2024/05/03 05:10:28
用公式求和：Sn=(x+1/x)^2+(x^2+1/x^2)^2+...(x^n+1/x^n)^2
用公式求和：Sn=(x+1/x)^2+(x^2+1/x^2)^2+...(x^n+1/x^n)^2
用公式求和：Sn=(x+1/x)^2+(x^2+1/x^2)^2+...(x^n+1/x^n)^2
Sn=(x+1/x)^2+(x^2+1/x^2)^2+...(x^n+1/x^n)^2
=x^2+1/x^2+2+x^4+1/x^4+2+x^6+1/x^6+2+...+x^(2n)+1/x^(2n)+2
=(x^2+x^4+x^6+...+x^(2n))+(1/x^2+1/x^4+1/x^6+...+1/x^(2n))+2n
=x^2(x^(2n)-1)/(x^2-1)+(1-x^(2n))/(x^(2n)(1-x^2))+2n
（x^2-x^(2n+2)+1-1/x^2n)/(x^2-1)+2n