1 Given that = n x" with convergence in (-1, 1), 1 X n=0 x find the power series for with center 0. 1 - 6x4 n=0 Identify its interval of convergence. The series is convergent from x = , left end included (enter Y or N): to x = , right end included (enter Y or N):

What is the interval of convergence of the power series (x-3)" 22 n=0

Does the series from 0 to infinity of (-1)^k/(2k+1) converge or diverge?

Determine whether the series ₁ (-1)^+¹n/2¹ converges or diverges. n=1

at) Find all the values of x such that the given series would converge. (-1)(x^)(n+ 4) (9) " The series is convergent from x = to x = n=1 , left end included (enter Y or N): right end included (enter Y or N):

What is the radius of convergence of the power series from 0 to infinity of (2x)^k?

Find the interval of convergence of the power series 3x" n2 n= IM:

Does the series from 1 to infinity of ((3n)/(1+8n))^n converhe or diverge?

Suppose that Cnxn converges when x = -4 and diverges when x = 6. What can be said about the convergence or divergence of the following series? n = 0 (a) When compared to the original series, we see that x = here. Since the original series: ---Select--- ifor that particular value of x, we know that this series ---Select--- (b) When compared to the original series, we see that x = here. Since the original series for that particular value of x, we know that this series ---Select--- ---Select-- (c) Cn(-2)" n= 0 When compared to the original series, we see that x = here. Since the original series for that particular value of x, we know that this series ---Select--- ---Select--- (d) (-1)"C,9 When compared to the original series, we see that x = here. Since the original series ---Select- for that particular value of x, we know that this series ---Select---

Does the series from n=1 to infiniity of (-1)^n(1+(1/n))^n converge or diverge using the alternating series test?