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Sequences and Series-Calculus for Engineers-Assignment, Exercises of Calculus for Engineers

Institute of Mathematics and ApplicationsCalculus for Engineers

This assignment is for Calculus for Engineers course. It was assigned by Prof. Adesh Rangarajan at Institute of Mathematics and Applications. It includes: Sequences, Series, Monotonic, Bounds, Limit, Value, Converges, Diverges, Determine, Conditionally, Absolutely, Power

Typology: Exercises

2011/2012

Uploaded on 07/23/2012

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Calculus II Assignment 03 February 21, 2009
Assignment – due on February 24, 2009 (submission time: 3:00 pm)
Late assignment will not be acceptable. No relaxation in policies.
(See “policies for assignments” on margala/yahoo group)
Question # 1
Part A
Determine whether the sequence is monotonic or not. Is the sequence bounded? If yes,
then what are the bounds?
2
cos
n
an
Part B
Determine whether the sequence is monotonic or not. Is the sequence bounded? If yes,
then what are the bounds?
n
nnea
Question # 2
Find the limit of the sequence
,...222,22,2
Question # 3
For what value of
p
does the series
2ln
1
npnn
converge?
Question # 4
Part A
Determine whether the series converges or diverges. Determine, where needed, whether
the series is conditionally convergent, absolutely convergent or divergent.
1/11
1
nn
n
Part B
Determine whether the series converges or diverges. Determine, where needed, whether
the series is conditionally convergent, absolutely convergent or divergent.
1!
1
nn
Part C
Determine whether the series converges or diverges. Determine, where needed, whether
the series is conditionally convergent, absolutely convergent or divergent.
1
1
sin)1(
n
n
n
pf2

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Calculus II Assignment 03 February 21, 2009

Assignment – due on February 24, 2009 (submission time: 3:00 pm)

Late assignment will not be acceptable. No relaxation in policies. (See “policies for assignments” on margala/yahoo group)

Question # 1

Part A

Determine whether the sequence is monotonic or not. Is the sequence bounded? If yes,

then what are the bounds?

cos

n 

an

Part B

Determine whether the sequence is monotonic or not. Is the sequence bounded? If yes,

then what are the bounds?

n an ne

 

Question # 2

Find the limit of the sequence

Question # 3

For what value of p does the series

 2 ln

n

p n n

converge?

Question # 4

Part A

Determine whether the series converges or diverges. Determine, where needed, whether

the series is conditionally convergent, absolutely convergent or divergent.

 1

11 /

n

n n

Part B

Determine whether the series converges or diverges. Determine, where needed, whether

the series is conditionally convergent, absolutely convergent or divergent.

n n

Part C

Determine whether the series converges or diverges. Determine, where needed, whether

the series is conditionally convergent, absolutely convergent or divergent.

1

( 1 ) sin n

n

n

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Part D

Determine whether the series converges or diverges. Determine, where needed, whether

the series is conditionally convergent, absolutely convergent or divergent.

n

n n

n

n

Question # 5

Part A

Find the radius of convergence and the interval of convergence of the power series

1 3.^6.^9 ...(^3 )

n

n n x n

n

Part B

Find the radius of convergence and the interval of convergence of the power series

  1

1

( 1 ) ( 1 ) n

n n

n n x n

e

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