Summary
Rules for convergent series
Convergence tests
comparison -> test against similar geometric series or p-series
ratio -> series involving factorials
root -> series involving the nth power
Useful logarithm for evaluating limits with exponents
Concept
Series
Sequence of partial sums, and its limit
divergent and convergent similar to sequences
Property of convergent series
Convergent geometric series
p-series
Bounded from above
Convergence of absolute series
else it is conditionally convergent
Application
Convergent geometric series
factorize to get n-1
Breakdown into partial sums for telescoping series
Alternating series test