Good morning, I needed Assistance with 5 and 6 thank you.

1. Determine whether or not the alternating series converge or diverge. o (_I)rHl @@ XF = nvn+1 > m42 b _I n ke R ( ) JE( ) 5\"2 2n+] 2. Determine whether the series converges absolutely, or converges conditionally, or diverges and give reasons for your conclusions. 5 D" n=13n+4 (b) 3(-0.2)" n=1 3. Use Ratio Test or Root Test to determine whether the following infinite series are absolutely convergent, or divergent. OPNSILES n=l| n2 03-2) n=2 ln n to the x3 term. 4. Calculate the Maclaurin series for f(x) = 5 1 +x 5. Find the interval of convergence for the power series o l S n=12n+1 . n n (b) E] Tia xn+| 6. Use substitution method and a known power series to find power series for f(x) = xcos(3x) . Please express your answer within one sigma notation