Is + 1/2^4 + 1/3^4 1/4^4 + ... + 1/N^4 = 1/N^4 + ... + 1/3^4 + 1/2^4 + 1? Consider the infinite series sigma_i = 1^infinity 1/i^4, this series converges and it converges to pi^4/90. One can try to approximate the infinite series by only adding a finite number of terms, and if the number of terms is large enough, then we could expect to have a good approximation. Compute the partial sums S_N = sigma_i = 1^N 1/i^4 = 1 + 1/2^4 + 1/3^4 + 1/4^4 + ... + 1/N^4 and the errors in the partial sums given by E_N = Exact - S_N (here Exact is pi^4/90). Let N at least reach 20, 000. Present your results in graphical form. Now compute the partial sums, but in the opposite direction (S_N = 1/N^4 + ... + 1/3^4 + 1/2^4 + 1). Again, compute the errors in the partial sums. Present your results in graphical form. Compare the results from parts 1) and 2)