Download PTU B.Sc CS-IT 2020 March 3rd Sem 71774 Sequence Series And Calculus Question Paper

Download PTU (I.K. Gujral Punjab Technical University Jalandhar (IKGPTU) B-Sc CSE-IT (Bachelor of Science in Computer Science) 2020 March 3rd Sem 71774 Sequence Series And Calculus Previous Question Paper

1 | M - 7 1 7 7 4 ( S 3 ) - 1 7 4 5
Roll No. Total No. of Pages : 02
Total No. of Questions : 07
B.Sc. (Computer Science) (2013 & Onwards) (Sem.?3)
SEQUENCE SERIES AND CALCULUS
Subject Code : BCS-302
M.Code : 71774
Time : 3 Hrs. Max. Marks : 60
INSTRUCTIONS TO CANDIDATES :
1. SECTION-A is COMPULSORY consisting of TEN questions carrying TWO marks
each.
2. SECTION-B contains SIX questions carrying TEN marks each and students have
to attempt ANY FOUR questions.

SECTION-A
1. Write briefly :
a) If a sequence is divergent to ? ?, then it is bounded below but not bounded above.
b) Prove that the sequence
3
1
n
is convergent.
c) Show that the series :

1 1 1
1 ______
1! 2! 3!
? ? ? ? is Convergent.
d) State Raabe?s test.
e) Prove that the series ? ?u
n
is divergent where u
n
=
1
n
n ?
.
f) State the first mean value theorem of integral calculus.
g) State comparison test in limit form for convergence of improper integral ( ) .
b
a
f x dx
?

at a.
h) Show that
6 2
0
45
.
8
x
x e dx
?
?
?
?

i) Express
3
2
1
2 3
0
(1 ) x x dx ?
?
as a beta function.
j) Compute
1
1
f dx
?
?
where ( ) f x x ? .
FirstRanker.com - FirstRanker's Choice
1 | M - 7 1 7 7 4 ( S 3 ) - 1 7 4 5
Roll No. Total No. of Pages : 02
Total No. of Questions : 07
B.Sc. (Computer Science) (2013 & Onwards) (Sem.?3)
SEQUENCE SERIES AND CALCULUS
Subject Code : BCS-302
M.Code : 71774
Time : 3 Hrs. Max. Marks : 60
INSTRUCTIONS TO CANDIDATES :
1. SECTION-A is COMPULSORY consisting of TEN questions carrying TWO marks
each.
2. SECTION-B contains SIX questions carrying TEN marks each and students have
to attempt ANY FOUR questions.

SECTION-A
1. Write briefly :
a) If a sequence is divergent to ? ?, then it is bounded below but not bounded above.
b) Prove that the sequence
3
1
n
is convergent.
c) Show that the series :

1 1 1
1 ______
1! 2! 3!
? ? ? ? is Convergent.
d) State Raabe?s test.
e) Prove that the series ? ?u
n
is divergent where u
n
=
1
n
n ?
.
f) State the first mean value theorem of integral calculus.
g) State comparison test in limit form for convergence of improper integral ( ) .
b
a
f x dx
?

at a.
h) Show that
6 2
0
45
.
8
x
x e dx
?
?
?
?

i) Express
3
2
1
2 3
0
(1 ) x x dx ?
?
as a beta function.
j) Compute
1
1
f dx
?
?
where ( ) f x x ? .
2 | M - 7 1 7 7 4 ( S 3 ) - 1 7 4 5
SECTION-B
2. a) Every cauchy sequence of real numbers is convergent.
b) if
Lim
n ? ?

1
,
n
n
a
l
a
?
? where 1, l ? then
Lt
n ? ?
a
n
= 0
3. a) Test the convergence of the series
2
2
1
1
n
n
x
n
?
?
?
.
b) if ?u
n
is convergent, show that ( 0, 1)
1
n
n n
n
u
u u
u
? ?
?
?
is also convergent.
4. a) Show that the series :

1 1 1 1
______
log 2 log3 log 4 log5
? ? ? ? is conditionally convergent.
b) State and prove cauchy?s general principle of convergence.
5. a) Prove that if a function is monotonic on [a, b], then show then it is Riemann
integrable on [a, b].
b) If 0 < x < 1, then show that
1
log (1 ) .
1
x
x x
x
?
? ? ?
?

6. a) Check for convergence the improper integral
1
1 1
0
(1 )
m n
x x dx
? ?
?
?
where m, n are real
numbers.
b) State and prove cauchy?s test for convergence of ( )
b
a
f x dx
?
at a.
7. a) Show that :

1 1 1
0
( , ) ; 0, 0
(1 )
m n
m n
x x
m n dx m n
x
? ?
?
?
? ? ? ?
?
?
.
b) Show that
1
( )
2
? ? ? .

NOTE : Disclosure of identity by writing mobile number or making passing request on any
page of Answer sheet will lead to UMC case against the Student.

FirstRanker.com - FirstRanker's Choice