SUNY Geneseo Department of Mathematics

Introduction to Infinite Series

Thursday, March 26

Math 222 01
Spring 2015
Prof. Doug Baldwin

Misc
- Colloquium
  - “Bodybuilding! ... for Mathematicians” + career reflections
  - Monday March 30, 4:00-5:00 pm, Newton 201
  - Extra credit for summaries
Questions?
Infinite Series
- Section 10.2
  - s_n = a₁ + a₂ + ... + a_n written as Sigma notation
    - aka nth partial sum
  - Infinite series is similar but continuing forever beyond a_n
  - Geometric series = a + ar + ar² + ... + ar^n-1 + ...
  - Sum, difference, constant multiple rules
- Examples
  - Sum of k
    - First few partial sums
    - Converge or diverge?
  - Sum of 3 / (7^k)
    - Sum of (3^k) / 7
  - Sum of (1/2)^k converges. To what?
  - What about sum of ( 1 + (1/2)^k )?
  - What about sum of 794 (1/2)^k?
    - = 794
    - By constant multiple rule
Next
- Introduction to convergence tests
- Read section 10.3 (“The Integral Test”)