Infinite Sequences and Series (BC Only)

$12

$8

$10

$14

$S' < S$

$S' > S$

$S = \frac{S'(R+K)}{R}$

$S' = \frac{SR}{R+K}$

The limit as $n$ approaches infinity of the terms is zero.

The corresponding series without alternating signs converges.

The terms decrease in absolute value to zero monotonically.

Each term is less than or equal to each term of a known convergent p-series where $p > 1$.

It can be represented as $f(x)=ar^n$ within interval $[c,d]$, where $|r|<1$.

The function must periodically continue at regular intervals across the entire real number line.

The integral $\int_{c}^{d} f(x) dx$ remains constant regardless of $x$ values within $[c,d]$.

$f'(x)+f''(x)=0$ between $(c,d)$.

14

-14

7

21

$\frac{32}{243}$

$\frac{64}{243}$

$\frac{8}{243}$

$\frac{16}{243}$

Its rate of growth will quadruple, altering its long-term behavior based on divergence or convergence criteria.

Doubling parameters doesn't change whether it converges or diverges; only magnitude changes are observed in sums where applicable.

Only its initial value will scale up, without affecting long-term behavior or convergence properties significantly for $|r| < 1$.

If initially convergent ($|r| < 1$), doubling these parameters makes it always diverge due to exceeding critical bounds for $r$.

6

$\frac{1}{2}$

3

2

100

150

125

50

$33\frac{1}{3}$

$31\frac{3}{4}$

$26\frac{2}{3}$

$50$