This is an optional module for those preparing for Engineering examinations Q-1) Do there exist distinct positive integers such that form an arithmetic progression (in some order)? Q-2) Define a sequence by , and for . a) Show that for and , divides b) If divides , show that divides . Q-3) Consider a nonconstant arithmetic progression . Suppose there exist relatively… Continue reading
Category: Algebra
Week -7 | Sequences & Series – 8
Practice problems MCQ questions can have more than 1 correct answer. Q-1) If are in HP, then are in a) A.P b) G.P c) H.P d) None of these Q-2) Find the value of Q-3) The value of is a) b) c) d) None of these … Continue reading
Week -7 | Sequences & Series – 7
This is an optional module for the students preparing for engineering entrance examinations Q-1) Show that tere cannot be an infinite AP, all of whose terms are perfect squares. Solution: Assuming that there exists such an AP, let denote the common difference of this progression. Thus can be represented as the difference of 2 perfect… Continue reading
Week -6 | Sequences & Series – 6
Q-1) Find the sum of , where . Solution: We have Q-2) Find the sum of Solution: We have the factors in the denominator in AP. In this case, what we normally do is to multiply and divide with the difference of the first factor and the last. Thus If we define , we have… Continue reading
Week -6 | Sequences & Series – 5
This is an optional module for the students preparing for engineering entrance examinations 1.1 Difference Equations By now that the difference between sequences and series is clear, we look at a new concept to solve recurrence relations related to sequences. Often we have our sequences defined by such a recurrence relation. For example, , with … Continue reading