Consider the following series,

1. Consider the series 2k -2+4+6+ ... (a) Compute the finite sums 2k, 2k, 2k, and 2k. The sequence cre- ated by these and subsequent values is known as the sequence of partial sums. (b) Let s, denote the nith partial sum of a series (Le. s, is the ath term in the sequence of partial sums). Here we see that s. = ) 2k; find a way to express s, as a function of n. (Hint: Recall our summation identities from Math 111.) (c) Given a series > as whose nth partial sum is s., consider lim an. We say that the series converges if this limit exists and call this value the sum of the series; otherwise we say the series diverges. Determine whether the given series converges or diverges