1+x/1+1+x²/2+1+x的四次方/4+1+x的八次方/8+...+1+x的n次方/n-1-x的2n次方/2n
来源:学生作业帮助网 编辑:作业帮 时间:2024/06/20 02:54:10
![1+x/1+1+x²/2+1+x的四次方/4+1+x的八次方/8+...+1+x的n次方/n-1-x的2n次方/2n](/uploads/image/z/986838-6-8.jpg?t=1%2Bx%2F1%2B1%2Bx%26%23178%3B%2F2%2B1%2Bx%E7%9A%84%E5%9B%9B%E6%AC%A1%E6%96%B9%2F4%2B1%2Bx%E7%9A%84%E5%85%AB%E6%AC%A1%E6%96%B9%2F8%2B...%2B1%2Bx%E7%9A%84n%E6%AC%A1%E6%96%B9%2Fn-1-x%E7%9A%842n%E6%AC%A1%E6%96%B9%2F2n)
1+x/1+1+x²/2+1+x的四次方/4+1+x的八次方/8+...+1+x的n次方/n-1-x的2n次方/2n
1+x/1+1+x²/2+1+x的四次方/4+1+x的八次方/8+...+1+x的n次方/n-1-x的2n次方/2n
1+x/1+1+x²/2+1+x的四次方/4+1+x的八次方/8+...+1+x的n次方/n-1-x的2n次方/2n
说好的加分哦!
现解答如下:
我们补一项到该式中:1/(1-x) 最后再减掉
那么:原式= 1/(1-x) +1/(1+x)+2/(1+x^2).-1/(1-x)
前两项合并 = 2/(1-x^2)+2/(1+x^2)+.-1/(1-x)
同上:= 4/(1-x^4)+.-1/(1-x)
同理得 = n/(1-x^n)+n/(1+x^n)-2n/(1-x^2n) -1/(1-x)
=2n/(1-x^2n)-2n/(1-x^2n)-1/(1-x)
=1/(x-1)
说话算数哦,加分吧!