2. Now consider the pseries DO 1 Z 16.- k:1 (a) For p : 0.5 and for p : 2, write the rst ve terms of the series. Then by studying partial sums using Sage, argue that one of these series converges and one diverges. Do not get too ambitious here on the number of terms, N, in your partial sums; depending on your computer system, you may be in for an annoying wait. Give an estimate of the sum of the convergent series. (b) Select two more p values, one of which gives a convergent p-series and the other a divergent one. Give explanations and evidence for your conclusions. (0) When p = 1 we get a special and important case of the p-series known as the harmonic Series, Go k=1 Write out and then compute the sum of the rst four terms of the harmonic series. Then use the computer to estimate the partial sums for N : 4, N : 128, and N : 1024 Wll' (d) Based upon your results of parts a and b, formulate a preliminary conjecture about conver- gence and divergence of the p-series in terms of the positive real number p