Calculus Series Tests

P-Test

1/n^p coverages when p>1 and diverges when p<=1

Geometric Series Test

a(r)^n converges when |r|<1 and diverges when |r|>=1

Nth Term Divergence Test

If lim(n→inf) a_n ≠ infinity, then a_n diverges

Integral Test

If a_n is continuous, positive, and decreasing then if int(n, inf) a_n dn is a finite #, a_n is convergent and divergent if not

Direct Comparison Test

Limit Comparison Test

If 0 < lim(n→inf) of a_n/b_n < infinity then their convergence is the same

Alternating Series Test

For a_n = (-1)^n b_n, if lim(n→inf) b_n = inf & b_n is decreasing, then a_n converges

Remainder Estimate Theorem for AST

If a_n converges by AST, then |R_n| <= b_n+1

Absolute Convergence Test

If |a_n| converges, so does a_n