MATH 212 Spring 2021— Exam 3 Part II
Instructor: Ching Wei Ho
Answer all questions. Show the steps of your computation. No credit will be given if you only give the
answer. You may use textbooks and notes during the exam, but communication with other persons (except the
Instructor or Assistant Instructors) and help from any other sources such as Internet are not allowed.
Upload and submit a single pdf file to canvas by the due time. If the AIs or/and I cannot read your work, you
will be given a 0 for this part.
1. Compute the sum of the following series.
(a) (4pt)
∞∑
n=1
41−n3n
(b) (4pt)
∞∑
k=1
(
1
k + 2
− 3
k + 1
+
2
k
)
2. Let {an} be the sequence defined by
a1 = 2, an+1 =
√
an + 5.
(a) (4pt) Show that an is an increasing sequence.
(b) (3pt) Show that an ≤ 3 for all n.
(c) (3pt) Does the limit
lim
n→∞ an
exist? Justify your answer. Find the limit if it exists.
3. (7pt) Sketch the curve
r = −eθ, −pi ≤ θ ≤ pi
and find its arc length.
1

欢迎咨询51作业君