Sequences, Series, and the Binomial Theorem flashcards

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In Arithmetic Sequences and Series, what does common difference mean?Arithmetic Sequences and Series: A sequence with fixed additive change.
Why use n−1 in the explicit rule?Arithmetic Sequences and Series: The first term is zero steps after itself.
In Arithmetic Sequences and Series, what does recursive rule mean?Arithmetic Sequences and Series: A next-term rule depending on a previous term.
What information must start a recursion?Arithmetic Sequences and Series: An initial term.
In Arithmetic Sequences and Series, what does finite arithmetic sum mean?Arithmetic Sequences and Series: A sum of evenly spaced terms.
Why can first and last be paired?Arithmetic Sequences and Series: Every symmetric pair has the same sum.
In Geometric Sequences and Series, what does common ratio mean?Geometric Sequences and Series: A sequence with fixed multiplicative change.
How does this differ from arithmetic?Geometric Sequences and Series: Arithmetic adds a fixed amount instead.
In Geometric Sequences and Series, what does finite geometric sum mean?Geometric Sequences and Series: The total of a fixed number of geometric terms.
Why treat r=1 separately?Geometric Sequences and Series: The usual formula would divide by zero.
In Geometric Sequences and Series, what does convergent infinite sum mean?Geometric Sequences and Series: A finite limit of infinitely many geometric terms.
What condition allows convergence?Geometric Sequences and Series: The common ratio must have absolute value less than one.
In Sigma Notation, what does index and bounds mean?Sigma Notation: A compact instruction to add indexed values.
How many integer indices run from 1 through n?Sigma Notation: Exactly n indices.
In Sigma Notation, what does expanding a sum mean?Sigma Notation: Turning summation notation into an explicit addition.
Why expand a few terms?Sigma Notation: It reveals the index-to-term rule and bound count.
In Sigma Notation, what does properties of sums mean?Sigma Notation: Linearity rules for finite sums.
Can different bounds be combined without adjustment?Sigma Notation: No, the included terms may differ.
In Pascal's Triangle and Binomial Coefficients, what does combination count mean?Pascal's Triangle and Binomial Coefficients: An unordered selection count.
When does order matter instead?Pascal's Triangle and Binomial Coefficients: For arrangements or assigned roles, use a permutation count.
In Pascal's Triangle and Binomial Coefficients, what does pascal recurrence mean?Pascal's Triangle and Binomial Coefficients: A recurrence among adjacent combination counts.
What are the outside entries of every row?Pascal's Triangle and Binomial Coefficients: They are one.
In Pascal's Triangle and Binomial Coefficients, what does binomial coefficients mean?Pascal's Triangle and Binomial Coefficients: The numeric factors attached to binomial terms.
Why do term exponents add to n?Pascal's Triangle and Binomial Coefficients: Each factor contributes exactly one u or v.
In Binomial Theorem and Applications, what does general term mean?Binomial Theorem and Applications: A specified term of a binomial expansion.
Why does C(n,k) appear?Binomial Theorem and Applications: It counts ways to choose the k factors contributing v.
In Binomial Theorem and Applications, what does selected coefficient mean?Binomial Theorem and Applications: Extracting a particular binomial coefficient.
What changes if v contains a number?Binomial Theorem and Applications: Its power contributes an additional numeric factor.
In Binomial Theorem and Applications, what does applied patterns mean?Binomial Theorem and Applications: A connection between algebraic powers and selections.
Do probabilities equal bare binomial coefficients?Binomial Theorem and Applications: No, event probabilities also need outcome probabilities and assumptions.