Infinite Sequences and Series (BC Only)

Replacing factorial with $(x-a)$ raised to a higher power maintaining differentiability of f.

Increasing n by one in all terms while keeping f differentiable at x = a.

Making f non-differentiable at every point near x = a.

Decreasing x by half towards approaching limit near center 'a'.

Changing the exponent on n from 1 to any number greater than or equal to one

Changing the exponent on n from 1 to exactly 2

Keeping the exponent on n as is without change

Changing the exponent on n from 1 to any number less than 1

The series converges only if the first term is negative

The sum of the series equals infinity

The Series converges

The series does not have a sum

$p = 1$

$p \leq 0$

$p > 1$

$0 < p \leq 1$

The sequence is a convergent sequence.

The sequence is a divergent sequence.

The sequence is a decreasing sequence.

The sequence is an increasing sequence.

$t_\infty$ is a convergent series.

It cannot be determined whether $t_\infty$ is convergent or divergent.

$t_\infty$ is a divergent series.

$t_\infty$ is neither convergent nor divergent

It converges because $-1 < r < 1$

Not enough information is given to determine convergence or divergence without knowing the first term's value

It diverges because $r > -\frac{1}{2}$ only ensures divergence for positive ratios

It diverges because $r < -1$

Ratio Test

Root Test

Integral Test

p-Series Test

The limit is 0

The limit does not exist

The limit is -10

The limit is 10

$\lim_{x \to \infty} \frac{f^{(a)}(xx)}{f^{(a)} + i(xx)n!}$

$\lim_{x \to \infty} \frac{|f^{(a)}(x)|}{|f^{(a)}(x+1)|}$

$\lim_{x \to \infty} \frac{f(f^{(a+n)}(x))}{f(n!(x))}$

$\lim_{x \to \infty} \frac{f^{(a)}(x)}{f(f^{(a)}(x))}$