If the series ∑ (n = 1) UN converges and the series ∑ (n = 1) VN diverges, try to prove that the series ∑ (n = 1) (UN + VN) diverges and find the detailed solution. Thank you

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• 1. The convergence of series UN ^ 2 is proved
• 2. Let the series un-un-1 converge and the series VN converge, and prove the absolute convergence of the series UN VN
• 3. Let the positive series ∑ UN and ∑ VN converge. It is proved that ∑ (UN + VN) ^ 2 also converges ……
• 4. 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
• 5. Prove Lim n →∞ n ^ n / (n!) ^ 2 = 0 by using necessary conditions of series convergence
• 6. Prove Lim n - > infinite n ^ n / (n!) ^ 2 = 0 by using necessary conditions of series convergence Please
• 7. 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
• 8. LIM (n →∞) un * n = 0, then the series ∑ UN converges?
• 9. 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?
• 10. Limit: LiMn →∞ (n-1) ^ 2 / (n + 1)
• 11. Excuse me: some problems of u = U1 + U2 (string) u = U1 = U2 (Union) Excuse me: u = U1 + U2 (string) u = U1 = U2 (parallel) I = I1 = I2 (string) I = I1 + I2 (parallel) Are the laws of these junior high school experiments only applicable to pure resistance circuits? Not a pure resistance circuit? More detailed points lead to deeper knowledge.
• 12. When U1 > 4, UN + 1 = 3un / 4 + 4 / UN, n →∞, UN → x, find X
• 13. Let U1 = 1, U2 = 1, UN + 1 = 2un + 3un-1 (n = 2,3,...) ) bn=Un/Un+1(n=2,3,…… ）Prove the existence of limbn, and discuss the convergence and divergence of series 1 / UN Here is my own solution The characteristic equation is R ^ 2-2r-3 = 0, R1 = - 1, R2 = 3, the general solution U (n) = C1 * (- 1) ^ n + C2 * 3 ^ n, UN = 3 ^ n-3 * (- 1) ^ n] / 6, then BN = 1 / 3, and then find the reciprocal of BN to get the divergence But I don't think it's right. Eigenvalue? Will solve, the original difference equation, I did not want to be detailed
• 14. Given the partial sum of series Sn = 2n / N + 1, find U1, U2, UN
• 15. Given U1 = 1, U2 = 2, find UN = 2U (n-2) + U (n-1) + 1 Solve how to deduce the general term formula
• 16. Why is the current I equal and the voltage u always = U1 + U2 +... UN when the circuit is in series
• 17. If ∑ UN converges, does ∑ u2n converge? Conversely, does ∑ u2n converge and ∑ UN converge?
• 18. It is proved that if the series ∑ UN satisfies (1) Limun = 0, (2) ∑ (u2n-1 + u2n) convergence, then ∑ UN converges
• 19. A series ∑ UN converges. How can we prove that its odd term ∑ u2n-1 also converges?
• 20. If the series UN converges to s, then the series (UN + UN + 1) converges to s