Math 106 BC Quiz 07 page 1 11/19/2010 Name
Circle your Section: B (11am) C (noon)
1a. Does the geometric series 2/3 + 4/9 + 8/27 + ··· converge? If so, to what?
1b. Explain whether the comparison test tells us that the series
∞
X
1
2k
3k+ ln kconverges, diverges, or is of no help, when
compared to the series in (1a). (Verify any inequalities you claim hold for the individual terms)
2a. Consider the series
∞
X
4
ak=√4/4 + √5/5 + √6/6 + √7/7 + √8/8 + ···. Use the integral test and an appropriate
function f(x) for which ak=f(k) to decide if the series diverges.
2b. If the series in 2a diverges, use the method in class which uses the corresponding integrals to find a Bfor which
PB−1
k=4 akis bigger than 20.
2c. Use your LHS program to actually find PB−1
k=4 akfor the Bin (2b).