Consider the series 1 n² +1 n=1 Which of the following is false? A) t is convergent by integral test B) It is convergent by ratio test C) It is convergent by nth term test D) It is convergent by limit comparison test E) It is convergent by direct comparison test

Q: (b) Prove that the real power series n!r" converges for only r 0. %3D

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Q: use the Limit Comparison Test to prove convergence or divergence of the infinite series.

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Q: Determine the convergence or divergence of the series.

A: To determine the convergence or divergence of the series.

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A: Your question has two-part we will solve the first part for you. Please resubmit the question with…

Q: 43. (n!)2 Σ (2n)! n=0

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A: Solution:-

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Q: 7. Determine if the following infinite series are absolutely convergent, conditionally con- vergent…

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Q: use the Limit Comparison Test to prove convergence or divergence of the infinite series.

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Q: e Almbert’s Ratio Test to the given series. Possible answers ar

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Q: Show that the series -1 (2n+1)" converges absolutely. in=1

A: We will check its convergence by ratio test .

Q: Show that the series n" n' is convergent. Deduce that lim (2n)! (2n)! n=1

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Q: The series Zan +... converges to 1 16 8 n = 1 Select one: True False

A: given ∑n=1∞ an = 12 -14+ 18-116+...   12-14+18-116+... ∑n=1∞-1n+12n= ∑n=1∞- -12n

Q: 6. Prove that if the power series E, akxk has a posi- tive and finite radius of convergence p, then…

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Q: use the Limit Comparison Test to prove convergence or divergence of the infinite series.

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Q: Show that the series 71 n' (2n)! is convergent. Deduce that lim 0% (2n)! n=1

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Q: Does the series 1+1/8+1/27+1/64+1/125+...(reciprocals of the perfect cudes) converge or diverge?…

A: Given series 1+18+127+164+1125+...... We can write the given series as 113+123+133+143+153+......

Q: Let n Prove converges. and Ž that the difference of these be goven fositive n%=D1 n= Seri es, Series

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Q: (b) Show that the interval of convergence of the series n=1 sest 2-12-1 (4n-3)² is given by

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Q: (a) Show that the series g(3) = E( 1 Z- NA z+ nA n=1 for every z # ma for any nonzero integer m and…

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Q: use the Limit Comparison Test to prove convergence or divergence of the infinite series.

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Q: Use the Ratio Test to determine whether the series is convergent or divergent. 6ke-k k = 1 Identify…

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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.

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Q: n²+n+1 En=1 n4+n² 00

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A: Given: The series is ∑n=2∞nln n.

Q: Use the Root Test to determine the convergence or divergence of the series

A: ∑n=1∞n2n+1n Here, an=n2n+1n

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Q: 134) Σ 1 * +1 ₂² n=1 ne"

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Q: 2. By taking the limit N 0o, argue that if -12" azn converges then so does -1 an. (Hint: apply the…

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