I need help please

1. In this problem you ll investigate the series 2 k_1 k2+k (a) Write out the rst 4 terms of the series. (b) Find the rst 4 partial sums of the series. Express them as simplied fractions. (c) Looking at your answer to (b), guess a formula for the n-th partial sum. ((1) Based on your guess from (c)1 does the series converge or diverge? If it converges, what is its sum? 3n 2n+lI 2. Consider the series 2 (ac. Suppose you know that the nth partial sum sn of the series is 1:1 (a) Find :11, a2, a3, and ak. (b) Does the series converge or diverge? If it converges, what is its sum? 3. In this problem, we will study the series Z ak = 2 (E kH) - 1.:1 (a) The lst partial sum is 51 | Q ,_. || .rx Dl|D' | |v- HE D. the 2nd partial sum is 32 l 7 81) + (% i i)' Write out the 3rd partial sum and the 4th partial sum. Do not simplify your answer Do you see any pattern? II D ._. + P. M II ,_. (b) Write down the n-th partial sum, 5\" using the - -- notation. (c) Simplify your answer in (b) and nd a closed formula for the nth partial sum1 3.\". (d) Is your answer in (c) the same as #1(c)? Does this make sense to you and why