MATH 101 Quiz #5 (v.T3)
Last Name:
Thursday, March 17
First Name:
Grade:
Student-No:
Section:
Very short answer question
1 1
1
1
1
1. 1 mark To what value does the series 1 + + +
+
+
+ · · · converge? Simplify
3 9 27 81 243
your answer completely.
Answer:
Short answer questions—you must show your work
2. 2 marks Find the solution to the separable initial value problem:
dy
3x2
= y ,
dx
e
y(0) = log 3.
Express your solution explicitly as y = y(x).
∞ X
6
6
3. 2 marks Show that the series
−
converges and find its limit. Simplify
2
2
k
(k
+
1)
k=1
your answer completely.
Long answer question—you must show your work
4. 5 marks The nth partial sum of a sequence {an } is known to have the formula sn =
1 + 3n
.
5 + 4n
(a) Find an expression for an , valid for n ≥ 2.
∞
X
(b) Show that the series
an converges. (It will help to make the expression from part (a)
n=1
a single fraction.)
(c) Find the value of the series
∞
X
n=1
an .