For each of the following series, use the sequence of partial sums to determine whether the series converges or diverges. OpenStax book is available for free at http://cnx.org/content/col11965/1.2 er 5 | Sequences and Series a. n+ 1

Q: Evaluate Σ n=1 2 2 n' +4n+3

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Q: Find the sum of the convergent series.

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Q: 1 Σ n%3D1 n

A: The given series is ∑n=1∞1n-1n2n To find: Find convergence or divergence of the series.

Q: evn+2 2+3 n=1

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Q: Find the sum of the series

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Q: 2 En=1 n(n+1)

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Q: α 4" n=2 5n!

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Q: 5 +1+ 1 | 5 + 1 25 + ..

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Q: = {()}. 2n 1 2n +1) T2 a) {a,} -

A: Given: To determine the series converges or diverges as follows, an=2n-12n+1n

Q: 28 85 K=I 5ks+ 8K²³-9 tk

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Q: 00 54. 3* k=1

A: Use ratio test

Q: 7+7+77+ 49 + to 12 terms

A: We need to find the sum of the series 7+7+77+49+... 12 terms. So,                  7+7+77+49+... 12…

Q: 3n+1 6n-1 n=0

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Q: 13) & 3{3} 1=1 ה DELL

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Q: Write a partial sum for the power series which represents this function consisting of the first 5…

A: Radius of converge of power series

Q: (-1)r+1 Vn + 1 n+ 1 10. -1)n+1, N=1

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Q: Decide if this series converges.

A: Result used:Limit comparison test:

Q: Find the sum of the series

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Q: Let an ;in 2 1 In(2" +1)' Determine if the sequence {an}n=1 is convergent or divergent. Determine if…

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Q: » Σ n=1 9 7 + 3n (In n)2

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Q: +1 ½ + 2 +..; S8 -> find the specified artial sum for each arithmetic series

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Q: find the sum of the series

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