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Sequences Series and the Binomial Theorem flashcards
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- What is common difference?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.
- What is recursive rule?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.
- What is finite arithmetic sum?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.
- What is common ratio?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.
- What is finite geometric sum?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.
- What is convergent infinite sum?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.
- What is general term?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.
- What is selected coefficient?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.
- What is applied patterns?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.