Convergent Series Test

Geometric Series

Look for a ratio like (1/4)^n

∣r∣ < 1 The series converges

∣r∣ ≥ 1The series diverges

Integral Test

Look for an easy integral, if the integral converges so does the series.

Alternating Series Test

If (-1)^n

and anything besides that is positive, and approach zero when going to infinity, the series converges.

Divergence Test

Set limit going to infity, if it does not approach 0.

Comparison Test

Use P-series and Geometric Series, if the function is smaller than a function where P or Geometric Converges, than that series must converge

P-Series

If p>1, the series converges

If p≤1, the series diverges

Limit Comparison Test

Make bn largest power on top over largest power on bottom, and figure out what bn is. then if the lim going to infinity if an/bn

is 0 < C < Infinity, then an matches bn

Root Test

Look for anthing to the power of n

L < 1, converges

L > 1 or L = Inf, Diverges

L = 1, nothing can be concluded

Ratio Test

Look for a geometric but not really.

L < 1 Converges

L > 1 or L = Inf, Diverges

L = 1, nothing.

Projection <a>, <a>

TBN

k(t)