Ans/ Diverged Q5/ For the following series :- 1 (x-2), (x- 2)² (x- 2)" 2n+1 f(x) + (-1)". 4 ......... 8 Find :- a- Values of (x) that make series converged b- The sum of series Ans./ a) 0

Q: What is the largest value of x for which the series (x - 8)" n 4 is absolutely convergent? Answer:

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Q: The interval of convergence of the power series (-1)*(x+2)" (n+1)422 OA -651s2. OB. None of the…

A: The given series is: ∑n=0∞(-1)n(x+2)n(n+1)422n...(1) Let, an=(-1)n(x+2)n(n+1)422n, n≥0

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Q: 6d. What does the above series 3(x - 1)" converge to for the values of x in the interval of conver-…

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Q: Determinee whether the series (1+ i) ( 5 ) is convergent or divergent by com- i=1 paring it to an…

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Q: V12(-1)" 3" (2n + 1) V12(-1)" 3" (2n + 1) 1. Consider the series ) Note: this was changed from n=0…

A: The given series is: ∑n=0∞12(-1)n3n(2n+1) which is an alternating series with an=12(-1)n3n(2n+1);…

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Q: For each series in questions (2)-(4), determine whether it converges absolutely, converges con-…

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Q: ∑∞ ((−1)^n−1(1−n)) /(3n−n^2) n=1 Find if the series converges or diverges! Find the limit if it…

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Q: By shifting the summation index of the following added series +00 +00 En(n-1),x"-4[n(n-1)C₁x"-2 +3 +…

A: Given that ∑n=2∞nn−1Cnxn−4∑n=2∞nn−1Cnxn−2+3∑n=1∞nCnxn+∑n=0∞Cnxn=0. Now, we only need to shift the…

Q: If the series 1(-1)" 2 were approximated using its first k terms, what would be the smallest number…

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Q: Consider the power series (x - 2) (x - 2)² 2 + (x - 2)³ 3 3. What is the radius of convergence? 1.…

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Q: _2. Which of the following series is divergent? 1 1 1 (α) Ση=12n-1 (b) En=1,3 (c) En=13 Σ n2 _3.…

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Q: O [(1+ v2)* k=0

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Q: (b) Determine whether the following series converge. If they converge then find their sum. E-1 (Use…

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