Question: Which of the following defines a convergent sequence of partial sums?
(a) Each term in the sequence is closer to the last term than any two prior consecutive terms.
(b) Assume that the sequence of partial sums converges to a number, L. Regardless of how small a number you give me, say ?, I can find a value of N such that the Nth term of the sequence is within ? of L.
(c) Assume that the sequence of partial sums converges to a number, L. I can find a value of N such that all the terms in the sequence, past the Nth term, are less than L.
(d) Assume that the sequence of partial sums converges to a number, L. Regardless of how small a number you give me, say ?, I can find a value of N such that all the terms in the sequence, past the Nth term, are within ? of L.