To test the series for convergence, you can use the P-test. (You could also use the Integral Test, as k=1 is the case with all series of this type.) According to the P-test: 1 converges k=1 00 1 O the P-test does not apply to k=1 8. 1 diverges k4 k=1 1 Now compute s5, the partial sum consisting of the first 5 terms of k=1 S5 =

Q: v that the series (-1)" is a conditionally convergent series. Then determine the least n=1 ber of…

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Q: Find the interval of convergence of (x - 15)2n+1 6n + 1 00 Σ n=15 (Use symbolic notation and…

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Q: q3 Determine if the series converges or diverges

A: Given: ∑n=2∞1n ln(n)

Q: Show that the series 2 - 2/4 + 2/9 - 2/16 ... is convergent by the alternating series test. and find…

A: The alternating series to be tested is ∑n=0∞(-1)n2(n+1)2.  Here, the nth term is an=(-1)n2(n+1)2 and…

Q: Comparison ust

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Q: ,1/2 Σ (n+1)"² 1/2 n=1

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Q: Use any method to determine whether the series converge. 1 (a) E + 14k + 1 This series diverges. k=1…

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Q: - Apply a test to determine whether the series 2 3" converges or diverges. n=1

A: We can use the ratio test here Since L>1 , so this series diverges.

Q: 2. Prove that the p-series converges for p > 1.

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Q: Use the Direct Comparison Test to determine the convergence or divergence of the series. 1 Σ 3n2 + 6…

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Q: 3. Determine whether the series converges. k +1 k²-2 k=1 (a) Converges (b) Diverges

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Q: 00 2) 3) n3+5n²-17 n en n n=1 n =2

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