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
Tag: CMI
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 – 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
A CMI Question
Q) We call a number as stable if there exists distinct natural numbers with such that . Show that if is stable, then so is . Hence, or otherwise find all stable numbers Solution: We assume that is stable. Thus there exists different natural numbers satisfying the given condition. We need to find distinct natural numbers… Continue reading
Week -5 | Sequences & Series – 3
1.1 Introduction to Convergence We have introduced the concept of infinite series’ in our previous modules. Today in this module, we shallt alk about convergence of an infinite series. Convergence, in elementary terms define the fact that the sum of an infinite series is bounded. This would mean . In other words let’s define . If… Continue reading