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

来源:学生作业帮助网 编辑:六六作业网 时间:2024/12/27 01:23:01
求sn=(1-2*5^-1)+(3-2*5^-2)+...+[(2n-1)-2*5^-n]求sn=(1-2*5^-1)+(3-2*5^-2)+...+[(2n-1)-2*5^-n]求sn=(1-2*5

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

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