k k+1 k=1 3. In this problem, we will study the series Z 01;, = Z ( ). (a) The 1st partial sum is 51 = (11: G a, and the 2nd partial sum is 52 a1 + (12: G % + (% %). Write out the 3rd partial sum and the 4th partial sum. Do not simplify your answer. Do you see any pattern? (b) Write down the nth partial sum, 3,, using the ' ~ ' notation. (c) Simplify your answer in (b) and nd a closed formula for the nth partial sum, .9". (d) Is your answer in (c) the same as #1(c)? Does this make sense to you and why