求和Sn=(a-1)+(a^2-2)+(a^3-3)+…+(a^n-n)?_数学解答

求和Sn=(a-1)+(a^2-2)+(a^3-3)+…+(a^n-n)?

人气：409 ℃　时间：2020-04-09 20:00:04

解答

(1/3*5)=(1/3-1/5)/21/(2n+1)(2n+3)=(1/(2n+1)-1/(2n+3))/2所以Sn=(1/3*5)+(1/5*7)+(1/7*9)+...+[1/(2n+1)(2n+3)]=0.5*[1/3-1/5+1/5-1/7+...+1/(2n+1)-1/(2n+3)]=0.5*[1/3-1/(2n+3)]