Question

5. (15 pts) Sinn a.) Apply the Divergence Test to this series. State your conclusion b.) Apply the Integral test. You should state the three conditions needed for c) but you may skip if possible, otherwise, say "no sum. 6. (20 pts) _ ( +1) a.) Determine converge diverge using one of the comparison tests. Justify every step b.) Find the correct partial fraction decomposition for a = Solve for the unknown constants in that partial fraction decomposition. C.) Rewrite the series by replacing a, by its partial fraction d.) Observe that the series is now a telescoping series, write out several terms, and determine convergence or divergence. Justify. e.) Find the sum of the series, if possible. Otherwise, say "cannot find sum." 7. Use the methods of Theorems 20—22. starting from the Reciprocal Power Series ( E X ), to find a power series for (x)= Simplify the term of the series and write the convergence condition