AP CAlc 10.1-10.2

A sequence is an ordered __________ of numbers.

list

The convergence or divergence of a sequence can be determined by examining its __________.

limit

An arithmetic sequence has a __________ difference between consecutive terms, found by subtracting __________ term from the __________ term.

common, previous, subsequent

A geometric sequence has a __________ ratio between consecutive terms, found by dividing __________ term by the __________ term.

common, subsequent, previous

The explicit rule for the nth term of an arithmetic sequence can be found using the formula __________.

a + (n-1)d

The explicit rule for the nth term of a geometric sequence can be found using the formula __________.

ar^(n-1)

A series is the __________ of the terms in a sequence.

sum

The sum of a series is the __________ to which the sequence of its partial sums __________.

limit, converges

A geometric series converges if the absolute value of the common ratio, |r|, is __________ than 1.

less

The nth term test states that if a series converges, then its nth term must approach __________.

zero

A Maclaurin series is a __________ series expansion of a function about __________.

Taylor, zero

The Maclaurin series for sin x is __________.

x - x^3/3! + x^5/5! - x^7/7! + ....

The Maclaurin series for cos x is __________.

1 - x^2/2! + x^4/4! - x^6/6! + ....

A Taylor polynomial is a __________ sum of a Taylor series, providing an approximation of a function.

partial