Infinite Sequences and Series (BC Only)

Divergent by Alternating Series Test.

Convergent by Ratio Test.

Convergent by Alternating Series Test.

Divergent by Root Test.

Find $\frac{dy}{dt}$ and $\frac{dx}{dt}$ and then take their quotient.

Differentiate $x(t) \cdot y(t)$ with respect to $t$.

Solve for $t$ in terms of $x$ and then differentiate $y$ with respect to $x$.

Integrate both $x(t)$ and $y(t)$ with respect to $t$.

Vingt

Zero

Un

Dix

Ratio test

Limit comparison test

Comparison test

Root test

Recalculate using Geometric Series Test.

Use Differentiation Test on all terms.

Test endpoints separately using tests for convergence.

Assume convergence based on Ratio Test alone.

It includes $x=5$.

It only converges at $x=5$.

It excludes $x=5$.

Its radius of convergence is necessarily less than or equal to 5.

The inverse functions if ($x=INV(f(t)), y=INV(g(t))$)

A single variable function representation.

A differential equation relating rates.

An equation relating $x$ and $y$, often called Cartesian or Rectangular Equation.

$\sum_{n=0}^{\infty} (3x)^n$

$\sum_{n=0}^{\infty} (x-1)^n$

$\sum_{n=0}^{\infty} \frac{(x+1)^n}{n^2}$

$\sum_{n=0}^{\infty} \frac{(2x)^n}{n!}$

Ratio Test

Geometric Sequence Test

Harmonic Series Test

Alternating Series Test

$\cos^n(\theta) + i\sin(n\theta)$

$\cos(\theta^n) + i\sin(\theta^n)$

$\cos^n(\theta) + i\sin^n(\theta)$

$\cos(n\theta) + i\sin(n\theta)$