Suppose that the nth partial sum of a series (∑∞n=1  an) is sn = (n+1) /( n+2). Is the series convergent or divergent? If it's convergent, find its sum.

Q: (-1)"(х + 3)" n2n n=1

A: We have to find

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Q: use the Integral Test to determine whether the infinite series is convergent.

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Q: 6. k ! ヒ=1

A: *to find:- whether the series convergent or divergent.

Q: Give an example of a divergent infinite series whose general term tends to zero.

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Q: Show that the function f determined by the nth term of the series satisfies the hypotheses of the…

A: Given that: ∑n=2∞1nlnn

Q: Determine whether the given series converges or diverges: Σ in=1 (1+2n²)"

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Q: Use the Ratio Test to determine whether the series is convergent or divergent. 00 (-7)" n2 n = 1…

A: RATIO TEST FOR SERIES: Let ∑n=1∞an be an positive term series and limn→∞an+1an = L ,           (i)…

Q: Determine whether the series is convergent or divergent. If it is convergent, n2 n=1 how many terms…

A: To find- If the given series is convergent.

Q: Determine whether the series is convergent or divergent by expressing the nth partial sum s, as a…

A: Expressing terms as a telescoping sum:∑n=4∞ 8n2-14∑n=4∞ 2(n+1)(n-1)4∑n=4∞ 1n-1-1n+1∑n=4∞…

Q: use the Integral Test to determine whether the infinite series is convergent.

A:

Q: (-5)"

A: According to question given ∑n=1∞-5nn2

Q: Apply the Ratio Test to show whether the infinite series is convergent or divergent n! Σ (-2)"

A: Given problem:-

Q: 8 Σ η=1 1 3Vn + n η

A: Calculate the limit of the given term as n reaches infinity.

Q: Find the interval and radius of convergence of the series whose nth term is (Зп )! ( 2n – 2 )! (6x -…

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Q: Use the Ratio Test to determine whether the series is convergent or divergent. 9n n = 1 Identify an-

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Q: 3. 5n3 +6 n=0

A: We have to find the given series which is convergent or not. ∑n=0∞3n3+7n5n3+6 It is known that if…

Q: Determine whether the series is convergent or divergent.

A:

Q: > sin n=1 2.

A: Explanation of the answer is as follows

Q: 7n Zn=1 n!

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Q: Determine whether the series is convergent or divergent. Ine пе n-1

A: According to the given information, it is required to check whether the given series is convergent…

Q: Give an example of a series such that > an converges but lan| diverges.

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Q: A series bn is called conditionally convergent if it converges and the corresponding series of…

A: A series  ∑bn is called conditionally convergent if

Q: Determine whether the series converges or diverges.

A:

Q: Determine whether the series is convergent or divergent. 2n=1 =1 (-1)"3n² 2 -1

A: Given series is ∑n=1∞(-1)n3n24n2-1

Q: Suppose that the nth term of the sequence of partial sums for a given series is Sn = 1+2n+3n² 4n²…

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Q: Show that the series whose nth term is n2 An 2n - 1 is convergent.

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Q: Determine whether the series is convergent or divergent by expressing the nth partial sum s, as a…

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Q: If aN is the nth digit in the decimal expression of 1/3, is the series convergent or divergent?…

A: According to the given information, An is the nth digit in the decimal expression. So, for the…

Q: Determine whether the series is convergent or divergent Σ nt +1

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Q: Determine whether the series is convergent or divergent by expressing the nth partial sum s, as a…

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Q: Use the Ratio Test to determine whether the series is convergent or divergent. (-6)" (2n + 1)! n = 0

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Q: Does the series from n=1 to infiniity of (-1)^n(1+(1/n))^n converge or diverge using the alternating…

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Q: Determine whether the series is convergent or divergent. Sn-1 6n – 1 n = 1 O convergent O divergent…

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Q: Determine whether the series converges or diverges. n-sn- 4 converges diverges

A: According to question given ∑n=5∞2nn-4

Q: Suppose a power series converges if | 4x - 8 | ≤ 40 anddiverges if | 4x - 8 | > 40. Determine the…

A: Given: A power series converges if | 4x - 8 | ≤ 40 and diverges if | 4x - 8 | > 40. To determine:…

Q: Suppose the partial sum sequence of a series is given by SN = N . Then the series converges.

A: Given the partial sum sequence of series is given by SN=1N

Q: Verify that the series Σ n=1 satisfies the conditions of the Integral Test, then use the Integral…

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Q: 48 3. (-1)"-

A: Solution is as below

Q: Determine whether the series is convergent or divergent by expressing the nth partial sum s,, as a…

A: We use Series integral method to find whether the series is convergent or divergent.

Q: What is the formula for the nth partial sum of the series? If the series is convergent, what is the…

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Q: (-4)" (2n +i)!

A: Ratio test of convergent

Q: Consider this infinite series: (n!)2 Σ n =1 (2n)! S = Use the Ratio Test to determine whether it is…

A: We have to find the given series is convergent or divergent. We have to apply the ratio test.

Q: Determine whether the series converges or diverges. sin2(n) n + 4 n = 1

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Q: Consider the series 00 n E In n + 2 n=1 Determine whether the series converges, and if it converges,…

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Q: Find the sum of the convergent series.

A: Given series : ∑n=0∞ -15n The given series is ∑n=0∞ -15n=1-15+125-1125+...... The given series is…

Q: Use the Root Test to determine whether the series 7k 2k +1 11. converges or diverges.

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Q: 27 1 2n + 1 n=1

A:

Q: Determine whether the series n+2 converges or diverges. Ln=1

A: Given: