MATH 101 Quiz #5 (v.T2)
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
5 25 125 625 3125
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
4x3
= y ,
dx
e
y(0) = log 5.
Express your solution explicitly as y = y(x).
3. 2 marks Show that the series
∞ X
2
i=1
answer completely.
2
−
3
i
(i + 1)3
converges and find its limit. Simplify your
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
.
3 + 2n
(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 .