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- If a power series ∞ n=0 anxn converges absolutely at a pointx0, then it converges uniformly on the closed interval [−c, c], where c = |x0|.Use the Cauchy Condensation test to prove that ∑ n = 2 to ∞ 1/( n (ln(n))^ p)) converges if p > 1 and diverges if p ≤ 1. (Make sure you verify that the hypothesis of the Cauchy Condensation test are met)Does the series from 1 to infinty of ((-1)^k*k)/(3k+2). converge or diverge?
- Use the Integral Test to determine if the series ∞ ∑ 1/n3 N=1 converges or diverges. Be sureto verify that the the conditions of the Integral Test are met.only 10,12,16: test the series of convergence/divergence.Apply the Cauchy’s n-th Root Test tothe given series. Possible answers are «convergent», «divergent», or «Cauchy’sn-th Root Test gives no information».