Warmup Problems #4 – Review for Test 2Math 1502, GrodzinskySeptember 13, 20131. Terminology review: complete the following statements.(a) A geometric series has the general form∑∞k=0. The series converges whenris less than oneand diverges whenris greater than or equal to one.(b) A p-series has the general form∑∞k=11kp.The series converges whenpis greater than oneand diverges whenpis less than or equal to one.To show these results, we can use theintegraltest.(c) The harmonic series divergesand telescoping series converge.(d) If you want to show a series converges, compare it to a largerseries that also converges.If you want to show a series diverges, compare it to a smallerseries that also diverges.(e) If the direct comparison test does not have the correct inequality, you can instead usethe limit comparisontest. In this test, if the limit is a finite, positivenumber (not equalto 0) then both series converge or both series diverge.(f) In the ratio and root tests, the series will convergeif the limit is less than 1 and divergeif the limit is greater than 1. If the limit equals 1, then the test is INCONCLUSIVE.(g) If limn→∞an= 0, then what do we know about the series∑kak?absolutely NOTHING!