Question

[(-1)^n(2n+1)/n]*x^2n的和函数

Answer 1

简单计算一下即可，答案如图所示

Answer 2

(2n+1)/n=2+1/n
=2∑(－x²)^n+∑(－x²)^n/n
=2/(1+x²)－∫2x∑(－x²)^(n－1)dx
=2/(1+x²)－∫2x/(x²+1)dx
=2/(1+x²)－ln(x²+1)