Question

麻烦会解大学数学微积分的同学帮忙速度解下，谢谢！（答案要的，最好解题过程也有）

Answer 1

Let an = (2n² + 3n)/√(5 + n⁷)
For large n，
an = 2n²/√n⁷
= 2/n^(3/2)
= 2√n³
Let bn = 2/√n³
lim(n→∞) an/bn
= lim(n→∞) [(2n² + 3n)/√(5 + n⁷)]/(2/√n³)
= (1/2)lim(n→∞) (2n² + 3n)n^(3/2)/√(5 + n⁷)
= (1/2)lim(n→∞) [2n^(7/2) + 3n^(5/2)]/√(5 + n⁷)
= (1/2)lim(n→∞) (2 + 3/n)/√(1 + 5/n⁷)
= (1/2) * (2 + 0)/√(1 + 0)
= 1 > 0
Since Σ(n=1→∞) bn = Σ(n=1→∞) 2/√n³ converges
By the Limit Comparison Test，
Σ(n=1→∞) (2n² + 3n)/√(5 + n⁷) also converges.

Answer 2

路过！！