微积分教学课件chapter8.5.ppt

So we denote Geometric interpretation: Example: Example: Estimating the sum of a series 11.6 Absolute Convergence and the Ratio and Root Test Example: Example: Example: 11.7 Strategy for Testing Series * For example: We can see that an alternating series can be written as: 8.5 Alternating Series,Absolute and Conditional Convergence Theorem: increasing bounded above Example: Solution: but So does not exist. Solution: Proof: Estimating sums: The error is smaller than the first neglected term. Theorem: Proof: is convergent. is convergent. Solution: is convergent. is absolutely convergent. is conditionally convergent. Solution: So the given series is absolutely convergent Example Determining Convergence or Divergence *