∑(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