高数题，无穷级数求解

Answer 1

因为这个级数的通项：
An = (2n+1)/[n²(n+1)²]
= [(n² +2n+1)-n²]/[(n²(n+1)²]
= [(n+1)² -n²]/[n²(n+1)²]
= 1/n² - 1/(n+1)²
所以，这个级数的和等于：
∑(2n+1)/[n²(n+1)²]
=∑[1/n² - 1/(n+1)²]
=1/1² - lim1/(n+1)²
=1 - lim1/(n+1)²
=1 - 0
=1
所以，正确的答案是 A