School

York UniversityDepartment

Mathematics and StatisticsCourse Code

MATH 1014Professor

AllStudy Guide

FinalThis

**preview**shows pages 1-3. to view the full**16 pages of the document.**Final Examination — April 14, 2012.

MATH1014

Name:

Surname:

Student Number:

Circle your instructor’s name: Moghadas Stepr¯ans Taylor

Question Mark Obtained

1 (a) (b) (c) (d)

2 (a) (b) (c) (d)

3

4

5

6

7 (a) (b) (c)

8 (a) (b) (c) (d) (e)

9 (a) (b)

Total Mark

Attempt all questions. You are allowed to use non-programmable calculators and refer to notes you

have prepared on a single sheet of 8.5 by 11 inch paper. Use the blank pages provided for rough work,

but show all relevant reasoning in the space provided. The time allowed for completion is 180 minutes.

Total marks: 138

The back of this page can be used for rough work.

Only pages 1-3 are available for preview. Some parts have been intentionally blurred.

Final Examination — April 14, 2012.

MATH1014

(1) Determine whether each inﬁnite series is absolutely convergent, conditionally convergent or

divergent. Explain your reasoning in each case by appealing to a relevant fact about inﬁnite

series.

(a)

∞

!

n=1

(−1)nn

√n+(−1)n6 marks

(b)

∞

!

n=210

(−1)nn2

2n6 marks

Only pages 1-3 are available for preview. Some parts have been intentionally blurred.

(c)

∞

!

n=1

n2+2

n

n3+3

n6 marks

(d)

∞

!

n=1

(−1)nsin(1/n)6 marks

(2) Let the function F(x)bedeﬁnedbyF(x)=

∞

!

n=1

x2n

n2if this series converges.

(a) Ignoring endpoints, what is the interval on which Fis deﬁned? 7 marks

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