Vx* +5x' +3 dx x' +2x? +4

Q: Ide being used. n'

A:

Q: 8 n1² Σ (2η)! n=1

A:

Q: Test for convergence/divergence, State the theorems used.

A: As per guidelines, I can answer only one question. Since questions are not interlink with each…

Q: find the interval of convergence.

A:

Q: (-3)" 2 3.5.7... (2n + 1) n=1

A:

Q: Test for convergence the series 3.6.9 ... 3n (i) E x" (x > 0), 7.10.13 ... (3n + 4) I1 = | 2.4.6 ...…

A:

Q: Prove the Continuity and Convergence Theorem.

A:

Q: Test for convergence the series 00 3.6.9 ... 3n (i) E x" (x > 0), 7.10.13 ... (3n + 4) 3D 0. 2.4.6…

A:

Q: tind the inderval of Conergence of the pacer Sevies nニ1

A:

Q: Use series to evaluate the limits

A: Given limit: limy→0y-tan-1yy3 Series for tan-1y, tan-1y=∑n=0∞-1ny2n+12n+1=y-y33+y55-y77+....

Q: 3 xp- ² - 4 12

A:

Q: i) n=1 1 1+2+3++n j) 1 n In n(ln(Inn)+1) k) 2" +n n!+1 n=1

A:

Q: · (−1)″ √2n+ 5 n³ +2n +4 n=1 t) Å sin(n) 3 n

A: Given series are: s) ∑n=1∞-1n2n+5n3+2n+4                            t)  ∑n=1∞sinnn3 To prove: Test…

Q: 19. 1 ntan-1 τη 20. Σ (-1)" n tan-1 in

A:

Q: Use series to evaluate the limits

A:

Q: Question 14: What is the value of In (det e) ?where A is a matrix given by A = 1 2 3 456 789 O 15 O…

A:

Q: n+1 4) Para la serie de potencias (x-2)** halla el intervalo de convergencia. a) (-2,6) b) [-2,6] c)…

A:

Q: Suppose that p(x)=an" converges on (-1, 1], find the interval of convergen n=0 8 left end included…

A:

Q: 27 n! n=0 converges to 0. 8.

A:

Q: en k%3D1 00

A: We will use Cauchy root test

Q: cos (n2) En=1 divergent. Determine whether the series is absolutely convergent, conditionally…

A:

Q: x" n n=0 n2

A:

Q: 5. Let an be a power series with radius of convergence 2 and note that the constant term is 0. Show…

A:

Q: a) b) 1 2 3 + 2.2 3.2² 4.2³ 1 1 1 1 + + 1.3 2.4 3.5 4.6 + + 4 5 5.24 6.25 1 + n(n+2) + + +. 1…

A:

Q: (-1)"(n² /n +3) (х-5)" 2" (n° +2) 3 n=1

A: