Mth 1002 Power Series Practice Material

CALCULUS 2 NAME: ________________________________

LAB 29 11.8 POWER SERIES Lab Time: ____________ Date: __________

Basic Guidelines:
Steps to determine the Radius of Convergence, R, and the Interval of Convergence, I:
n 1
u
(1) Apply the Ratio Test for Absolute Convergence nlim  L and force L  1 .
  u
n

(2) Solve the inequality to find I ( B, C ) (the open interval of convergence).
(3) Determine the convergence at each endpoint to see if they are included in I.

Determine the radius and interval of convergence for the following power series.

3n
1.  (n  2)
n 0
2 xn


n n n 1 n 1
a n   3 2 x  an  1   3 2 x
n 2 n 3
n 1

lim 33 n  nn 32 2 
n 1 2 x
a n 1
lim an n
n  n x
2
 lim 3 nn2 64 nn94  x  311  x  3 x
n

Force limit  1  3 x  1  x  13
Center : 0 Radius : 13
  0  ,0  1
3
1
3
    13 , 13 
Need to check endpoints x  13 and x  13