1/3+1/15+1/63+1/255+1/1023+--+1/(2^n+1)(2^n-1)求和

来源：学生作业帮编辑：作业帮分类：数学作业时间：2024/05/09 14:27:00

=1/(3*1)+1/(5*3)+.+1/(2^n+1)(2^n-1)
=(1/1-1/3)/2+(1/3-1/5)/2+.+[1/(2^n-1)-1/(2^n+1)]/2
=[1/1-1/3+1/3-1/5+...+1/(2^n-1)-1/(2^n+1)]/2
=[1/1-1/(2^n+1)]/2
=[2^(n-1)]/[2^n+1]

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