http://www.ck12.org Chapter 8. Infinite Series

1

( 1 −x)( 1 − 2 x)= (^1 +x+x

(^2) +...)( 1 + 2 x+ 4 x (^2) +...)
= 1 + 3 x+ 7 x^2 + 15 x^3 +...by the above result

∞
n∑= 0 (^2 n+^1 −^1 )xn.
Exercises

1. Find the first 4 terms of a power series for√( 1 +x^1 )( 1 + 2 x).


2. Find a power series for( 1 −rx)(^11 −sx)wherer,s>0 are real numbers and
   a.r 6 =s
   b.r=s.