Test

Equations Page

Ratio Test

$$\lim_{n \rightarrow oo}\left | \frac{a_{n} + 1}{a_{n}}\right |$$

Nth Term Test

$$\lim_{n\rightarrow oo}a_{n} \neq 0$$

Geometric Series Test

$$\sum_{n = 0}^{oo} a * r^{n-1}$$

a) $$s_{oo} = \frac{a}{1 - r}$$

Telescoping Series Test

$$\sum_{n = 0}^{oo} \frac{1}{f(x) * g(x)}$$

Harmonic Series Test

$$\sum_{n = 1}^{oo} \frac{1}{n}$$

Integral Test

$$\sum_{n = 0}^{oo}a_{n}$$

P-Series Test

$$\sum_{n = 1}^{oo} \frac{1}{n^p}$$

Limit Comparison Test

$$\lim_{n\rightarrow oo} \frac{a_{n}}{b_{n}} = c$$

Direct Comp

$$0 \leq a_{n} \leq b_{n}$$ 1) $$a_n$$     2) $$b_n$$

Alternating Series Test

$$\sum_{n = 1}^{oo} (-1)^{n-1} a_{n}$$

a) $$a_{n} \geq a_{n + 1} \geq 0$$    b) $$\lim_{n \rightarrow oo} a_{n} = 0$$

Root Test

$$\lim_{n \rightarrow oo} (a_{n})^{\frac{1}{n}}$$