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
Tag: JEE Advanced
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
Week -5 | Sequences & Series – 2
1.1 Logarithms of Progressions and basic properties We define the natural logarithm of a postive number as . Logarithm of a negative number is not defined. Let’s recollect the basic properties of natural logarithms: Ex -1 If be 3 reals in GP, show that are in HP Solution: We have , which implies are in AP.… Continue reading
Week -5 | Sequences & Series – 1
1.1 Introduction to Series & Sequences In Mathematical Analysis, a sequence is defined to be an ordered collection of terms/objects. This colelction or list can either be finite, or infinite. Thus we have both finite & infinite sequences. Often we define sequences by a recursive formula with some base conditions. Thus let’s consider with is… Continue reading
Week -4 | System of Equations – 6
Practice Problems (MCQ Questions may have more than 1 correct answer) Q-1) Solve the equation in reals . Q-2) If , be the roots of the equation , then the value of is a) b) c) d) None of these Q-3) Let be such that has no real roots. Show that the… Continue reading