This preview shows page 1. Sign up to view the full content.
Unformatted text preview: note on p. 699 for more details. 2. (3 pts) Show that the following series is divergent or Fnd the sum: ∞ ± n =2 1 n 21 Using the techniques of partial fractions (details are omitted here), we Fnd that 1 n 21 = 1 / 2 n11 / 2 n +1 . Then for large enough k , this becomes a telescoping sum: s k = k ± n =2 1 n 21 = k ± n =2 ´ 1 / 2 n11 / 2 n + 1 µ = k ± n =2 1 / 2 n1k ± n =2 1 / 2 n + 1 = k1 ± n =1 1 / 2 nk +1 ± n =3 1 / 2 n s k = 1 / 2 1 + 1 / 2 21 / 2 k1 / 2 k + 1 = 3 41 / 2 k1 / 2 k + 1 ±rom this we see that lim k →∞ s k = 3 / 4, so the sum converges to 3/4 ....
View
Full
Document
This note was uploaded on 10/20/2010 for the course MATH 53903 taught by Professor Christ during the Spring '09 term at University of California, Berkeley.
 Spring '09
 CHRIST

Click to edit the document details