This assignment will count the same as a WeBWorK homework and is due 11/8 at the beginning
of class. I expect clear thinking with COMPLETE sentences and proper grammar. Typing is
not required, but nice handwriting is appreciated.
1.
2.
(5 points) Suppose that lim nan = 1. Prove that
n→∞
(5 points) Prove that if
∞
P
∞
P
an diverges.
n=1
an is a convergent series of positive terms then
n=1
(5 points) Prove that if an > 0 and lim (an )1/n = R then
diverges if R > 1.
n→∞
ln(1 + an )
n=1
converges.
[Hint: consider the function f (x) = x − ln(1 + x)]
3.
∞
P
∞
P
n=1
an converges if R < 1 and