2. (Uniform convergence) Show that if a >, then the series is uniformly convergent on R. nº (1+ nz²)

Q: Find the interval of convergence for the given power series. (ӕ — 10)" Σ п(-9)" n=1 The series is…

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Q: Test the for being series Convergenk divergent or 8. Vn In n

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Q: 2. Prove that the series n"(1 + na") n=1 converges uniformly on every finite interval in R if a >.…

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Q: Check the convergence of the series sin(1/n)

A: The given series is  ∑n=1∞sin1n To check the convergence of the given series , we require few…

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Q: find the interval of convergence and the radius of convergence for the series.

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Q: sin(n+ n 2/ un3D0 1+vn

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Q: Find the radius and interval of convergence of the series. X=∞ and n=0 n!/2n + 1*x^n

A: Radius of converges is 0 And interval of converges is {0}

Q: Find the interval of convergence of the following series: x5 x7 X- + +... 7 all values of x O -2<xs2…

A: The radius of convergence is the largest interval in which the series is known to converge.

Q: n'+1 Vп+1-уп-1 a) En=1 b) Σ 1 п3+1 п

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Q: n=1 √n 3 n° +1

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Q: Determine if the series is divergent or convergent 5/4 using P-series test n=1 4n n²

A: To determine whether the following series is divergent or convergentby using p-series test.

Q: Ax) = 4 – x?

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Q: Find the radius of convergence and the interval of convergence of the power series (-2)" 2n + 1 n=0

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Q: A power series is convergent if and only if x is in the interval (-2,8]. The power series is…

A: A power series is convergent if and only if x is in the interval (-2,8] therefore, interval of…

Q: n=0 2√ñ 3n " Σ(−1)n ln(n) n n=1

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Q: ) Find all the values of x such that the given series would converge. (-1)"x" 11"(n² + 11) The…

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Q: * 3" +n 2) Use the Comparison Test to determine whether the series or divergent. Show All Your Work.…

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Q: (a) If {an}=1 and {b„}n=1are both sequences of real numbers where 0 < an < bn and En=1 bn diverges,…

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Q: Let {S,} be sequences, find the radius of convergence of power series (a) S, =* 2m 2" m=1 210m…

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