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
Tag: ISI
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 -4 | System of Equations – 7
This is an optional module for the students preparing for engineering entrance examinations Q-1) Let be a positive integer such that is prime. Choose for , such that the are not all equal. Also let be a polynomial such that for all . Show that the degree of is at least . Q-2) Let be distinct integers.… Continue reading
Week -4 | System of Equations – 5
This is an optional module for the students preparing for engineering entrance examinations Q-1) Find the number of natural numbers which satisfy the following 2 conditions: a) b) divides Solution: , this is divisible by for any natural number 2. Note that for any number to be divisible by , it must be divisible by its… Continue reading
Week -3 | System of Equations -3
This is an optional module for the students preparing for engineering entrance examinations Polynomials 1.1 Introduction We have already given an introduction to polynomials in our earlier chapters in this module. For any polynomials & , there exists poynomials & such that with . Note that in this case the degree of can be as well. Thus, … Continue reading