c) Determine whether each series is convergent or divergent. If it is convergent, find its sum. a) 00 n=1 2n-1 3n+1 b) Σ n=1 sin 1 00 3”+1 Σ. n=0 4" d) 00 n=0 -3n e) 1+ e + + e3 + 4 +... For what value or values of a, if any, does the given series converge? Σαν a>0, b>0 an+b' n=1 Determine whether each series is convergent or divergent. Carefully explain your reasoning. 1+2" 1+3.2" n=1 b) Σ n-1 n=0 13√n². +1

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A: Given, ∑n=1∞1n2+11n+30 To evaluate sum of series if it exists

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Q: 3 9 Using sigma notation, write the following expression as an infinite series: 1+ − + · 4 16 n2+ 1…

A: By using sigma notation, to write the following expression as an infinite series.1+34+916+2764+...

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A: Concept:

Q: Suppose that Σ an = -3 and n=] ∞ A. Σ(-6an + −8bn) n=1 = B. (-6an +-8bn) n=2 = ∞ n=1 bn = -5 and a1…

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Q: 3) Use the integral test to determine whether the following series is convergent or divergent. Σ n+6…

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Q: Find the nth term an of the given infinite series for which n = 1, 2, 3,... 1 12 1 9 + 1 10 + 1 11 +

A: Given

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Q: 2).  For an as follows, write the sum        an as a geometric series. a1 =  1 14 and  an an + 1

A: This is a question of infinite series.