Homework 25 – Power Series 1) Show that the power series a) – c) have the same radius of convergence. Then show that (a) diverges at both endpoints, (b) converges at one endpoint but diverges at the other, and (c) converges at both endpoints. a) 13nnnxb) 13nnnxn c) 213nnnxn 2) Find the radius and interval of convergence. a) 0nnnx b) 03nnnx c) 013!nnnxn d) 0!5nnnnx e) 211531nnxn f) 21112nnnnxn g) 5117nnnnx h) 122nnnex 3) Use 011nnxx for 1x to expand the function in a power series with center 0c and determine the interval of convergence. a) 15fxx b) 3116 2fxx 4) a) Use differentiation to show that 2111nnxnx for 1x . b) Use the result in a) to evaluate 12nnn. 5) a) Use the power series for xye to show that 11112! 3! 4!e b)
View Full Document
Unlocking...