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