Theory 1
It can help to associate certain “strategy tips” to find convergence tests based on certain patterns.
Matching powers → Simple Divergence Test
Use the SDT because we see the highest power is the same (
) in numerator and denominator.
Rational or Algebraic → Limit Comparison Test
Use the LCT because we have a rational or algebraic function (positive terms).
Not rational, not factorials → Integral Test
Use the IT because we do not have a rational/algebraic function, and we do not see factorials.
Rational, alternating → AST, and LCT or DCT
Use the AST because it’s alternating. Then use the LCT (to find absolute convergence) because its a rational function.
Factorials → Ratio Test
Use the RaT because we see a factorial. (In case of alternating + factorial, use RaT first.)
Recognize geometric → LCT or DCT
Use the LCT or DCT comparing to
because we see similarity to (recognize geometric).