Multiple Choice (1 pt each) Circle the correct answer. 1. A sequence { an } is (a) a pattern (b) a function of a real variable c) a function whose domain is the natural numbers (d) a function whose range includes only the natural numbers 2. Let {an } be a sequence and dn. = vn. Then a3 is (a) undefined, since the range of a sequence includes only the natural numbers. (b) V3 (c) the partial sum of the first three terms of { an } d) the limit of an as n - 3 3. A sequence { an} converges to a number _ if (a) by taking n sufficiently large, we can make an, as close as we like to L (b) by taking n arbitrarily large, we can make a,, as close as we like to L (c) by taking n sufficiently close to L, can make an as large as we like (d) by taking n arbitrarily close to L, we can make an, as large as we like 4. A partial sum s,, of a series is (a) An incomplete sum (b) The sum of the first n terms of a sequence (c) The noth term of a sequence summed n times (d) The limit as n - co of the sum the first n terms of the sequence 5. The sum of an infinite series exists if (a) the limit of the sequence of partial sums diverges as n -> co (b) the limit of the sequence of partial sum converges as n (c) the initial terms of the sequence are values close to 0 (d) the tail terms of the sequence are values close to 0