The series ∞ (-10) k k! k=1 is an alternating series but we can apply the ratio test to ∞ (-10) k k! to test for absolute convergence. Applying the ratio test for absolute convergence you would compute ak+1 lim k→∞ ak = lim = k→∞ Hence the series converges

Q: 8 Σ Ο /6n6 + 10n4 – 11 (2n + 1)2(3η – 2)2

A: Given sequence is ∑0∞6n6+10n4-11(2n+1)2(3n-2)2 Here, the nth term is Tn=6n6+10n4-11(2n+1)2(3n-2)2…

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Q: To test this series for convergence 00 n3+5 where p- You could use the Limit Comparison Test,…

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A: First simplify as shown below.

Q: (iv) Σ (−1)n+¹ (n+m)³ • n,mEN Explain here briefly what absolute convergence means for the double…

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A: In the given question, the sequence is given as: xk=121.9k

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A: Find the radius of convergence.

Q: For what values of x does the series converge absolutely 1 inVn 3" 2 4"x2n n(x + 3)" nx" Σ n=0 4"(n?…

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Q: +00 Suppose that E a, has positive terms and its partial sums s, n=1 +00 an satisfy the inequality…

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Q: 8. Consider the series 22 31-n (a) List the first five partial sums of this series. (b) Determine if…

A: To calculate the required partial sums and discuss the convergence of the series

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Q: If k-P converges, then k-p+0.001 converges. k=1 k=1

A: If ∑k=1∞k-p converges, then ∑k=1∞k-p+0.001 converges.

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Q: (b) Determine the convergence of the series a, for the following cases: 4r2-3r +2 2r4 +r2 +10' 3r+5…

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Q: 8 Consider 2-³. This is deceptive, and it is tempting to cal- n=0 = culate B lim sup(2-¹)¹/n = and…

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Q: (a) If {an}=1 and {b„}n=1are both sequences of real numbers where 0 < an < bn and En=1 bn diverges,…

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