ob 12. E n-1 n5" n=1

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

A:

Q: Test the series for convergence or divergence. (-1)" n3 + 4 converges

A:

Q: (n!)²3" -(x)" Σ n = 1 (2n)!

A: Use ratio test for Radius of converges

Q: 8 Σ (2x)" n = on + 4

A: The summation of the (2x) n/(n+4), n from 0 to infinity.

Q: Determine the radius and interval of convergence for the following power series. 8 n=1 (-1)"n 4" -…

A:

Q: Determine the convergence or divergence of the series

A: ∑n=1∞3nn3 Here, an=3nn3⇒an+1=3n+1n+13

Q: 1 What is the radius of convergence for the power series for 1+ 5x Input your answer as a decimal.

A: Here we find the radius for power series convergence.

Q: 8 ξ Σ n = 0 (7x)" n + 8

A:

Q: Determine the interval of convergence of the power series: n=1 (-1)" (-1)" n 3" A. A single point x…

A:

Q: Find the interval of convergence of the series: El- 1)-5"(2n + 1)! (z + 5)" 00 6" (n!)² n=1 3 Radius…

A:

Q: 8 (3x)" Σ n = on + 4 n+4

A: Summation of (3x) n/(n+4), n from 0 to infinity.

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

A:

Q: n=1 (4x-1)" n2

A:

Q: (-1)"n!(r- b)" 8n n-1

A: