2. Use the integral test to determine whether or not the series E f(n), n=1 where f(n) conditions that a function f must satisfy before the integral test can be applied, and show that f(x) = 1/x does satisfy these conditions. 1/n", p > 1, is convergent. As part of your answer, state the three

Q: n Use the integral test to decide whether the series - n²+1 converges or diverges. We determine…

A:

Q: 8. Determine whether the series is conditionally convergent, absolutely convergent, or divergent: 1…

A: Explanation of the solution is given below..

Q: p for which In (n) Comvenges

A: Given∑n=1∞ln(n)np

Q: If the series En=1 an converges absolutely, the sequence {b,} is bounded, then the series sin(a,)b,…

A: ∑ann=1∞ is absolutely convergent and bn is bounded .

Q: Find the sum of the convergent infinite series 3"+1 Σ 7" n=0 s = 25/6 O s = 15/4 O s = 21/4 O s =…

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Q: 1 n * (In n) n=2 8.

A:

Q: Find the largest interval (in x) where the series summation from n = 1 to infinite of xe-nx…

A: Here we use D'Almbert ratio test.

Q: M8 =M 8. (a) (n" - an) (b) In (2 + an)

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Q: 8. (c) 2+ an+1 In 2+ an (d) In (1+ an) n

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Q: Solve Σ 0 to ∞ ((n! • x^n)/ n^n) for x = e and x = -e and explain whether each point converges or…

A: Solve for x = e and check whether it converges or diverges as follows.

Q: Use the Ratio Test to determine whether the series is convergent or divergent. 00 n! 86 n = 1…

A: See the detailed solution below.

Q: 1. Find a Maclaurin Series for f(x)=sin(3x). 2. Find a fourth-degree Taylor polynomial for f(x)=…

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Q: 1. Find a power series representation for the function f(x) = 5x2- Determine the interval of…

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Q: Is the sum from n=1 to infinity of sin(n) convergent, conditionally convergent or divergent?

A: The problem is asking us to determine whether the infinite series ∑n=1∞sin(n) is convergent,…