作业帮1又1/2＋3又1/4＋5又1/8＋···＋[(2n-1)+1/2的n次方]=
来源：学生作业帮助网 编辑：作业帮 时间：2024/05/05 21:18:46
![1又1/2＋3又1/4＋5又1/8＋···＋[(2n-1)+1/2的n次方]=](/uploads/image/z/2581145-17-5.jpg?t=1%E5%8F%881%2F2%EF%BC%8B3%E5%8F%881%2F4%EF%BC%8B5%E5%8F%881%2F8%EF%BC%8B%C2%B7%C2%B7%C2%B7%EF%BC%8B%5B%282n-1%29%2B1%2F2%E7%9A%84n%E6%AC%A1%E6%96%B9%5D%3D)
1又1/2＋3又1/4＋5又1/8＋···＋[(2n-1)+1/2的n次方]=
1又1/2＋3又1/4＋5又1/8＋···＋[(2n-1)+1/2的n次方]=
1又1/2＋3又1/4＋5又1/8＋···＋[(2n-1)+1/2的n次方]=
=[1+3+……+(2n-1)]+(1/2+1/4+……+1/2^n)
=[1+(2n-1)]*n/2+1/2*(1-1/2^n)/(1-1/2)
=n²+1-1/2^n