1.1 Evaluating expressions by Differentiation Often, we would need to call up Calculus to compute Binomial Expressions and sums. We’ll represent as from here on. Let’s consider a small example: Ex -1: Show that Solution: If the positive integers appear as the product of Binomial coefficients, then that’s a hint that the problem may be… Continue reading
Tag: Engineering
Week – 16 | Binomial Theorem – 2
1.1 Basics of the Binomial Theorem , where . This is what we call the Binomial Theorem, and holds for all reals . In the above theorem, if we put , we arrive at the following identity: . Combinatorially speaking, out of a set of elements, the total number of ways that a selection can be formed… Continue reading
Week – 15 | Binomial Theorem – 1
1.1 Introduction to elementary Calculus formulae To thoroughly study and understand this module on Binomial Theorem, we’ll need to understand a couple of basic notations of Calculus and Number Theory to begin with. We’ll cover these topics in detail later on, when the time is right, but for now, let’s concentrate on arming ourselves with… Continue reading
Week -15 | Probability Theory – 5
Q-1) Two players A and B want respectively m and n points of winning a set of games ; their chances of winning a single game are p and q respectively, where the sum of p and q is unity ; the stake is to belong to the player who first makes up his set… Continue reading
Week -15 | Probability Theory – 4
Q-1) A 5-digit number is formed from the numbers 1,2,3,4,5 without repetition. Find the probability that the number is divisible by 4. Solution: A number is divisible by 4 if and only if the last 2 digits of the number is divisible by 4. Thus these numbers must have the last 2 digits as 24… Continue reading