3.) Consider the following formula for the sum of the first n terms of a geometric series. Itrtrz+ ... + pn-1_ 1 - rn 1 - r (a) Setr = -x2 in the formula above and rearrange to show that 1 1+x2 =1- x' + x4- x6+ ...+ (-1)n-1x2n-2+ (-1)nx2n 1 + x2 (b) Integrate both sides of the equation in part (a) over [0,1] to show that . + . + (-1)n-1 72n 2n - 1+(-1)n/ 1 + x2 ax (c) Verify that x2n that 74x2 - x" and use this and the Comparison Theorem for integrals (page 361, comparing definite integrals) to show 72n OS 1 1 + x2 dx s OL 2n + 1 (d) Prove that = 1 WIH 4 + 7 + ... Hint: Use parts (b) and (c) to show that the partial sums Sn satisfy Sn - " s and conclude that lim Sn = ". n- co