lim(x→∞){ 1/(1*3)+1/(3*5)+...+1/[(2n-1)(2n+1)] }=?_数学解答

lim(x→∞){ 1/(1*3)+1/(3*5)+...+1/[(2n-1)(2n+1)] }=?

人气：172 ℃　时间：2020-06-07 14:57:33

解答

1/(1*3)+1/(3*5)+...+1/[(2n-1)(2n+1) =[2/(1*3)+2/(3*5)+...+2/[(2n-1)(2n+1)]/2 =[(1/1-1/3)+(1/3-1/5)+……+(1/(2n-1)-1/(2n+1)]/2 =[1-1/(2n+1)]/2 =1/2-1/(4n+2) 所以lim(x→∞){ 1/(1*3)+1/(3*5)+...+1/[(2n-1...