NOTE: YOU ARE NOT ALLOWED TO USE LIMIT COMPARISON TEST & ALTERNATING SERIES TEST +00 sin' n +00 n(In n)3 Σ n2 +2-n n=2 n=1 W!

Q: find the lourent's series for function f(z)= ((z^2)-3z+2)^(-1) 0</z-1|<1

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Q: What is the correct power series form of f(x) =/1-3x³ at a-0? * (1·3.5..· (2n- 3))· 3^x³n Σ n=0 2" -…

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Q: The series O True O False Σ (-1)^+1 n=2 n3+1 is absolutely convergent.

A: The given series is summation of (-1)n+1/(n3+1), n from 2 to infinity.

Q: A/ Show that as a half range series of cosine terms for 0 < x < 1, π² /cos 2x cos 4x cos 6x +- +…

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Q: Consider the series ∞∑n=0 n4−3/3+n5 How would you do limit comparison test on this one?

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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: 2 + In n Use the Comparison Test to determine if the series E converges or 2 n=1 _n sin'n diverges.

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Q: To test this series for convergence 4" + 6 7n ∞ n=1 You could use the Limit Comparison Test,…

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Q: oVイhe Set of Convengence of the Power series 2,2" (x-9) is; n°(5+6^) -(6.12) - (3. 15) - [3.15] -[6,…

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Q: Find the sum of E n(n + 1)x" = for < x </

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Q: Questions 12-15: Determine if each series converges or diverges. Indicate which test you are using…

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Q: Give a power series representation for the following tanh^-1 x

A: We have given that , fx = tanh-1x We need to find Power series expansion of fx. We know that ,…

Q: The series O True O False (-1)^ n Σn=1 is conditionally convergent.

A: Given a series ∑n=1∞an .  If ∑n=1∞an converges, but the corresponding series ∑n=1∞an  does not…