series-flowchart by Brown

# series-flowchart by Brown - Comparison Test or use Limit...

This preview shows page 1. Sign up to view the full content.

Convergence/Divergence of X n =1 a n lim n →∞ a n = 0 ----→ NO ----→ X a n Diverges by Divergence Test YES p -Series: a n = 1 n p ----→ YES ----→ X 1 n p ± Converges , if p > 1 Diverges , if p 1 NO Geometric Series: a n = ar n - 1 -→ YES -→ X n =1 ar n - 1 = a 1 - r ( Converges ) , if | r | < 1 Diverges , if | r | ≥ 1 | NO | Alternating Series: a n = ( - 1) n - 1 b n -→ YES -→ Use Alternating Series Test , or Use Ratio/Root Test to see if Converges Absolutely | NO Use Other Convergence Tests: (1) If a n behaves like a p-series or Geometric series, usually use
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: Comparison Test or use Limit Comparison Test . Find appropriate b n to compare. (2) If a n involves factorials, usually use Ratio Test , L = lim n →∞ ² ² ² ² a n +1 a n ² ² ² ² . (3) If a n involves n th powers throughout, usually use Root Test , L = lim n →∞ n p | a n | . (4) Integral Test ....
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online