Please answer all of the following questions. Thank You!

3. (15 points) 4 a) Decompose (4n-3) (4n+1) into partial fractions. 4 b) Hence, find the nth partial sum of the series Zn=1 (4n-3)(an+1) c) Hence, determine whether the series converges or diverges. If it converges, find its sum.4. (10 points) Determine whether the following series converge or diverge. Give reasons for your answer. n un=1 3n+5 b) Zn=1 47-1 c) 2n=12 d) yo 1 1 n45. (10 points) Use the comparison test or the limit comparison test to test the convergence of the series M=16. (10 points) Use the integral test to test the convergence of the series In n 1=1(10 points) Use the Alternating Series Test to show that the series is convergent: 2\")\" n=1 V\" 8. (25 points) Investigate the convergence of the following series: nen a) >co 2n=1 (1+2n2)n b) Zn=1