MAT021C - Spring
Quiz 1 - 04.09.15
Name:
Student Id:
Show all work clearly and in order. Circle your final answers.
Justify your answers algebraically whenever possible.
Problem 1. Show that
lim
n→∞
ln n
= 0,
nc
for any positive constant c.
Problem 2. Assume that the following sequence converges and find its limit
1
1
1
2+
, ...
2, 2 + , 2 +
1,
2
2+ 2
2 + 2+1 1
2
Problem 3. Express
2.0202020202 . . .
as an infinite series, find the sum (limit) of the series, and thereby express it as a quotient of two integers