求1-1/2+1/3-1/4+1/5-1/6+.+1/(2n-1)-1/2n=?n→∞_数学解答

求1-1/2+1/3-1/4+1/5-1/6+.+1/(2n-1)-1/2n=?n→∞

人气：418 ℃　时间：2020-04-26 01:17:37

解答

当n=>∞时
S=ln2
1-1/2+1/3-1/4……+1/2n
=1+1/2+1/3+1/4……+1/2n-2(1/2+1/4+……+1/2n)
=1/(n+1)+1/(n+2)+……1/2n
=1/n(1/(1+1/n)+1/(1+2/n)+……+1/(1+n/n)
=1/(1+x)[从0积到1]=ln2