Consider the series Σ n=1 (2x)n n2 A) According to the Ratio Test, for what two values of x is the test inconclusive? B) Test the two values of x which were identified in Part(d) for convergence or divergence? Justify your answers.

Q: 3. Determine whether the series n +1 3n2n n=1 converces or diverges.

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Q: )c) Find the sum of each of the following series. (i) )ii) (iii) n = 2 8 n = 2 8 n = 1 n(n – 1)x",…

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Q: Use the alternating series remainder estimate to find what value of n required to estimate the…

A: First we shall state the ALTERNATING SERIES REMAINDER ESTIMATION result. If the alternating series…

Q: Q.2 Find the interval of convergence of the power series ( E-0 x2n) and find the sum of the series…

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Q: 1. Use the Alternating Series Test to determine whether the series Σ(-1)"+¹ converges absolutely,…

A: Alternating Series Test: A series ∑an where an=-1n+1bn where bn≥0, ∀n is convergent if (i)…

Q: Part 2. Express the power series below into a single summation. 2. (x + 2) E nan(x + 2)"-4 – E nan(x…

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Q: 7. Determine whether the series Σn=1 n 5n 6n+2 is convergent or divergent.

A: Necessary condition for convergence  :                         Necessary condition for…

Q: c. If the series has a sum, find the sum.

A: -12Explanation:If you have any questions let me know in comment box thankyou for your question.

Q: 3. Find the exact value of the series S = > n(n +2)* n=1

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Q: 11) Find the sum of the series. 1 n(n + 3) Σ n=1

A: The given series is:  ∑n=1∞ 1n(n+3)

Q: 3. Give an example of divergent series n=1dn and Ln=1 6n for which the series ("q + "p) converges.

A: Given: that An example of divergent series ∑n=1∞ an and ∑n=1∞ bn for which the series  ∑n=1∞ an+bn…

Q: Q5// A. Draw a graph with the degree sequence 1, 1, 6, 4, 4. B. Consider the function b(n) = 4n+3…

A: This is a multiple part question . The solution to the given questions are explained below.

Q: 1 3 (1+m²)²

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Q: Determine whether the series 3 (²) Σ 3(cos nm) n=0 n is convergent or divergent, and if convergent,…

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Q: +∞ Determine whether the series n=1 3n+1 ln(n is convergent or diverger

A: Given ∑n=1∞n23n+1ln(n+1) L-Hopital's Rule. When the limit of the quotient function is in the…

Q: Σ n² – 3n + 2 n=3

A: Explanation of the answer is as follows

Q: Find the sum of the series 1 1 n +1 n +3 n=1 5 (B) (C) 1 (D) (E) 3. (A) 112

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Q: 4. The series n=0 1-5m² n *** (a) is Absolutely Convergent (b) is Conditionally Convergent, but not…

A: Solution:-

Q: 5. Use geometric series to show that: 1 (a) Σo(-1) k = 1 if−1 < x < 1 1 (b) Σ(x-3) = ¹ if 2 < x < 4.…

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Q: n (n2 + 1)2 n=1

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Q: Evaluate the series 7 E (n² – 5) n=1 44 O "Do You Want to Build a Snowman" -4 105

A: We have to evaluate the series: ∑n=17n2-5 Putting given values of n into the summation, we get…

Q: Show that for |x| < 1, 1+2x =1+x – 2x2 +x³ +x* – 2x³ + x® + x7 – 2,* + - 1+x+x? Hint: Write F(x) as…

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Q: Consider the series (-1)+112n-1 n=1 (n+5)3 11+2 In this problem you must attempt to use the Ratio…

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Q: State where the power series is centered Σ (-1)"(x – 4π) 9η - (9n)! n = 0

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