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
Week -6 | Sequences & Series – 4
1.1 Introduction to infinite series’ We have introduced the concept of infinite series’ in our last modules. We have also briefly talked about the convergence of an infinite Geometric Series. The concept of convergence of a series is something that we have taken up in our advanced section of this module. To give an idea, here… 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