CO1

• Geometric Series converges if _


  |r| < 1
• Geometric Series diverges if _


  |r|>1
• $∑ ar^k=$$a+$$ar+$$ar^2+$$...+$$ar^k$


  Geometric Series
• The sum of a Geometric Series

  $∑ ar^k=$$a/1-r$
• How to solve Telescoping Sums


  Using Partial Fraction Decomposition, then input the k values.
• $∑ 1/k =$$1+$$1/2+$$1/3$


  Harmonic Series
• It is a divergent series

  Harmonic Series
• $∑ 1/k^p =$$1+$$1/2^p+$$1/3^p$


  Hyperharmonic or P-series
• P-series converges if


  P > 1
• P-series diverges if


  0 < P < 1
• In divergence test the series diverges if


  $uk ≠ 0$
• In divergence test, if uk = 0 it


  diverges or converges, inconclusive
• How do we know when Integral Test is applicable?

  If the series is decreasing
• Informal principle in comparison test

  Constant terms in the denominator can be deleted
• In limit comparison test, the series both converges or diverges if


  p is finite and > 0
• In Ratio Test, the series converges if

  p < 1
• In Ratio Test, the series diverges if

  p > 1 or infinity
• In Ratio Test, the series is inconclusive if


  p = 1
• In Root Test if p < 1, the series

  converges
• In Root Test, if p > 1 or infinity, the series


  diverges
• In Root Test if p = 1, the test is

  inconclusive
• $Σ (-1)^(k-1)$


  Alternating Series
• $Σ (-1)^k$


  Alternating Series
• An alternating series converges if 


  $a_1>a_2>a_3>a_4$
• An alternating series converges if the limit is

  equal to zero
• In absolute convergence, a series is said to converge absolutely if

  If the series of absolute values converges
• The ratio test can be used on any series with positive terms.
• A conditionally convergent series is one that converges but does not converge absolutely.