Binomial Theorem
1. A sentence is called a statement if it can be adjudged as true or false. Every statement is a sentence, but a sentence may or may not be a statement. 2. A statement involving natural number n is generally denoted by P(n). 3. A binomial is an algebraic ex..
Binomial Theorem
Introduction - A binomial is an algebraic expression of two terms which are connected by the operations '+' or '-'. For n = 1,2,3,4, the expansion of (a + b) n , has been expressed in a very systematical manner in terms of combinatorial coefficients. The above expression suggest the conje..
Introduction - A binomial is an algebraic expression of two terms which are connected by the operations '+' or '-'. For n = 1,2,3,4, the expansion of (a + b) n , has been expressed in a very systematical manner in terms of combinatorial coefficients. The above expression suggest the conje..Binomial Theorem for Fractional Index
Binomial Theorem for Fractional Index - For any rational number n, We accept this expansion without proof. The restriction on x is not required when n is a natural number. Now, we shall see that when n is a natural number, then the above expansion coincides with that as given ea..
Binomial Theorem for Fractional Index - For any rational number n, We accept this expansion without proof. The restriction on x is not required when n is a natural number. Now, we shall see that when n is a natural number, then the above expansion coincides with that as given ea..Binomial Theorem Introduction
Introduction - A binomial is an algebraic expression of two terms which are connected by the operations '+' or '-'. For example, x - y, a + 3b, x 3 + 4y etc. are binomials. We know that, For n = 1,2,3,4, the expansion of (a + b) n , has been expressed in a very systematical mann..
Introduction - A binomial is an algebraic expression of two terms which are connected by the operations '+' or '-'. For example, x - y, a + 3b, x 3 + 4y etc. are binomials. We know that, For n = 1,2,3,4, the expansion of (a + b) n , has been expressed in a very systematical mann..Bayes Theorem, Binomial and Poisson Distributions
Introduction - Suppose the two events are not independent, that is the occurrence of one depends on the occurrence of other, then how do we compute This can be explained by conditional probability. Baye's theorem is named after the British mathematician Thomas Bayes who published it in a ..
Introduction - Suppose the two events are not independent, that is the occurrence of one depends on the occurrence of other, then how do we compute This can be explained by conditional probability. Baye's theorem is named after the British mathematician Thomas Bayes who published it in a ..Some Applications of Binomial Theorem for Fractional Index
If x be numerically so small that its square and higher powers may be neglected, then (1+x) n = 1+nx (approximately), because x 2 , x 3 , x 4 ,. are all approximately zer..
Binomial Nomenclature
Binomial Nomenclature - It is the system of giving a scientific name to an animal or a plant, an outstanding system contributed by Carolus Linnaeus. According to this system, any given animal or plant is given a scientific name consisting of two words. The first word refers to name of the..
Binomial Theorem Application for Positive Integral Index
Theorem - Using Binomial theorem, prove tha..
Theorem - Using Binomial theorem, prove tha..Alternative Proof of Binomial Theorem for Positive Integral Index (Combinatorial Method)
Alternative Proof of Binomial Theorem for Positive Integral Index (Combinatorial Method). We have, (a + b) n = (a + b) (a + b) ....... n times. The terms on the RHS are obtained by taking one letter from each factor and multiplying them together. Choosing 'a' from all the..
Use binomial theorem to find the expansion of (1 - x)5
Use binomial theorem to find the expansion of (1 - x) 5 => 1 - 5x + 10x 2 - 10x 3 - 5x 4 + x 5 or 1- x + x 2 - x 3 + x 4 - x 5 or 1 - 5x + 10x 2 - 10x 3 + 5x 4 - x 5 or 1- x 5..
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