abscissa n math

Let a = First term, r = common ratio, n = number of terms. Multiply both sides of (i) by r, the common ratio. Subtracting (ii) from (i), we get ..

To insert n Harmonic Means between two given quantities - Let a and b be two given quantities. It is required to insert n harmonic means h 1 , h 2 , h 3 ,....h n between the quantities a and b. Let d = common difference of the A.P. Hence h 1 , h 2 ,....h n..

We observe that the index of r on the right hand side is one less than the suffix of t on the left hand side in each of the equalities. Hence t n = ar n - 1 which is the general term of the given G..

Let n be a positive integer. The continued product of first n natural numbers is called factorial n and is denoted as n..

C(n,r) = C(n,n-..

Strictly speaking 0! has no meaning. But since n P n = n! we may understand 0! = ..

The number of circular permutations of n different objects is (n-1)..

A set of numbers arranged in a definite order according to some definite rule is called a sequence. or A sequence is a function whose domain is the set N of natural numbers. It is customary to denote a sequence by a letter 'a' and the image a(n) or t(n), n ..

Let A be a square matrix of order n. If there exists a matrix B of order n such that AB = BA = I, where I is the identity matrix of order n, then the matrix A is said to be invertible and B is called the inverse (or reciprocal) of ..

The selection of a number of things taking some or all of them at a time are called combinations. The number of ways of selecting r things out of n dissimilar things is denoted by C(n, r) or n C ..