C0900TextPages_page_78

C0900TextPages | page 78 | https://thedailydialectics.com/pdfs/education/C0900TextPages/C0900TextPages.pdf

670 CHAPTER 9 Infinite Series EXAMPLE | Finding a Geometric Power Series Centered at 0 Find a power series for f(x) = ya? centered at 0. Solution Writing f(x) in the form a/(1 — r) produces 40 2 _ a 2+x 1-(-x/2) 1-r which implies that a = 2 and r = —x/2. So, the power series for f(x) is 4 oo xt+2—…