LiMn →∞ (1 + 2 + 3 +...) n-1)/n²

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• 13. Finding limit LiMn →∞ (n-1) ^ 2 / (n + 1) Limit: LiMn →∞ (n-1) ^ 2 / (n + 1) Is to find the limit of the square of (n-1) divided by (n + 1) when n approaches infinity I think we can use that formula, that is, n tends to infinity, and the limit is determined by the degree of N, because the upper side is the square of N, and the lower side is the first power of N, so I think it should be ∞ But the answer is + ∞. How does that work out? The upper part of the fractional line should be approaching positive infinity. Will the positive infinity of the answer come like this This is not a series limit problem, just a common function limit problem, there should be no statement that n must approach positive infinity, right?
• 14. LIM (n →∞) un * n = 0, then the series ∑ UN converges?
• 15. Find the convergence and divergence of a series. LIM (n tends to infinity) is one of the nth power of the sum of 1 + 1 / N. find the convergence and divergence of this series
• 16. Prove Lim n - > infinite n ^ n / (n!) ^ 2 = 0 by using necessary conditions of series convergence Please
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• 18. Let LIM (n →∞) na_ N exists and the series ∑ (n = 1 →∞) n (a)_ n-a_ It is proved that the series ∑ (n = 1 →∞) a is convergent_ N convergence
• 19. Let the positive series ∑ UN and ∑ VN converge. It is proved that ∑ (UN + VN) ^ 2 also converges ……
• 20. Let the series un-un-1 converge and the series VN converge, and prove the absolute convergence of the series UN VN