1-1/2+1/3-1/4+1/5-1/6+.（共无数项）求和答案是ln2,只用高等数学,不用编程,

Question

1-1/2+1/3-1/4+1/5-1/6+.（共无数项）求和
答案是ln2,只用高等数学,不用编程,

Answer 1

当n=>∞时
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