TestFlowChart - Series Convergence\/Divergence Flow Chart TEST FOR DIVERGENCE Does limn an = 0 an Diverges NO YES p-SERIES Does an = 1\/np n 1 Is p > 1

TestFlowChart - Series Convergence/Divergence Flow Chart...

This preview shows page 1 out of 1 page.

Series Convergence/Divergence Flow Chart TEST FOR DIVERGENCE Does lim n →∞ a n = 0? a n Diverges NO p -SERIES Does a n = 1 /n p , n 1? YES Is p > 1? YES a n Converges YES a n Diverges NO GEOMETRIC SERIES Does a n = ar n - 1 , n 1? NO Is | r | < 1? YES n =1 a n = a 1 - r YES a n Diverges NO ALTERNATING SERIES Does a n = ( - 1) n b n or a n = ( - 1) n - 1 b n , b n 0? NO Is b n +1 b n & lim n →∞ b n = 0? YES a n Converges YES TELESCOPING SERIES Do subsequent terms cancel out previous terms in the sum? May have to use partial fractions, properties of logarithms, etc. to put into appropriate form. NO Does lim n →∞ s n = s s finite? YES a n = s YES a n Diverges NO TAYLOR SERIES Doesan=f(n)(a)n!(x-a)n? NO Isxin interval of convergence? n =0 a n = f ( x ) YES Try one or more of the following tests:NO Pick{bn}. Doesbnconverge? Is 0anbn?anConvergesYES Is 0bnan?NONOanDivergesYES

  • Left Quote Icon

    Student Picture

  • Left Quote Icon

    Student Picture

  • Left Quote Icon

    Student Picture