求解高等数学,敛散性!!

2025-06-27 17:54:57
推荐回答(1个)
回答1:

(n+1)/(2n^3-1) = 2 + ∑(n+1)/(2n^3-1)
= 2 + ∑(n-1+2)/(2n^3-1)
= 2 + ∑(n-1)/(2n^3-1) + ∑2/(2n^3-1)
< 2 + ∑(n-1)/(n-1)^3 + ∑2/(n-1)^3
< 2 + ∑1/(n-1)^2 + ∑2/(n-1)^3
不等式右边正项级数收敛, 左边级数必收敛