Sequences and Series flashcards

Question 1

What is a sequence?

Accepted Answer

A sequence is a function whose domain is the positive integers (or a subset), producing an ordered list $a_1,a_2,a_3,\dots$.

Question 2

State the arithmetic series sum formula $S_n$.

Accepted Answer

$$S_n=\frac{n}{2}(a_1+a_n)=\frac{n}{2}\bigl(2a_1+(n-1)d\bigr)$$
$S_n$ is the sum of the first $n$ terms.

Question 3

When does an infinite geometric series converge, and what is its sum?

Accepted Answer

It converges when $|r|<1$, and then
$$\sum_{k=1}^{\infty} a_1 r^{k-1}=\frac{a_1}{1-r}.$$

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