8/13/2019 Infinite Series Paper Mid Term 2013

1/1

Dr Tariq Mahmood 13-Dec-13

Prof. @ CHEP

Created by: Ramay & Co.

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Mid term

BSc (3rd

Semester)

Morning/Evening

Infinite Series and sequence

Student Name: Roll #:

Question#2: Solve the following questions as per instructions. (10 Marks)

a) Find a formula for nth term of the Sequence. ( 2 Marks)an= 0, 1, 1, 2, 2, 3, 3, 4, 4,

b) Write out the first five terms of the sequence by using given 1 sttwo terms along with arecursion formula. ( 2 Marks)

a1= 2, a2=

1, an+2=

c) Let {an} and {bn} be the sequence of real numbers and let A & B be real numbers. Thenprove that lim (.)= A.B if = A and = B. ( 2 Marks)

d) Define and prove the sandwich theorem. (4 marks).Question#3: Which of the sequences {an} converge and when diverge? Find the limit of each

convergent sequence. (10 Marks)

a)An = (-1)n1 d)an= tan h(n)b)An = e)an = () c) An = 3

Question#4: Solve the following questions as per instructions. (5 Marks)

a) Write the 1stfew terms of each series to show how the series starts. Then find the sum ofthe series. +

() . (2 Marks)

b) Use the partial fraction to find the sum of the given series. (3 Marks) 40(2 1)(2 + 1)

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