Video Notes Review: Sequences and Series (Garbled Transcript)

Vocabulary flashcards derived from the garbled notes, focusing on key terms related to sequences and series.

n

Number of terms in a sequence or the size of a dataset; examples in the notes include n = 15 and n = 12.

r

Common ratio or rate of change in a sequence; examples show r = 1 or r = -1; there may be conditions like 'if r = -1, n is even'.

S

Sum of a sequence or series; often denotes the total of terms up to a given index (partial sum).

S1

First partial sum in a series (the sum of the first term or initial segment of terms).

T

Term of a sequence (the nth term) or a placeholder for a single term in a sequence.

Even

An even number is divisible by 2; used as a condition for n or indices in sequence problems.

Subscript notation

Using subscripts to index elements in sequences or series (e.g., S1, 9₁) to denote specific terms or sums.

DATE

A heading or label on the page, likely indicating a date or section marker in the notes.

Example

A worked demonstration illustrating a rule or computation mentioned in the notes.

n

Number of terms in a sequence or the size of a dataset; examples in the notes include n = 15 and n = 12.

r

Common ratio or rate of change in a sequence; examples show r = 1 or r = -1; there may be conditions like 'if r = -1, n is even'.

S

Sum of a sequence or series; often denotes the total of terms up to a given index (partial sum).

S1

First partial sum in a series (the sum of the first term or initial segment of terms).

T

Term of a sequence (the nth term) or a placeholder for a single term in a sequence.

Even

An even number is divisible by 2; used as a condition for n or indices in sequence problems.

Subscript notation

Using subscripts to index elements in sequences or series (e.g., S1, T1, or a_1) to denote specific terms or sums.

DATE

A heading or label on the page, likely indicating a date or section marker in the notes.

Example

A worked demonstration illustrating a rule or computation mentioned in the notes.

Application of variables in problem solving

The variables n, r, S, and T are fundamental in setting up and solving problems involving sequences and series, allowing for the calculation of specific terms, sums, or properties of the sequence based on given conditions.

The specific numerical value or general expression derived for an unknown variable (e.g., n, r, S) or an unknown term (e.g., T_k) that satisfies the given conditions of a sequence or series problem; it is the outcome of the solving process.