solve maths sum integers

>If any two rows or columns of a determinant are equal, then its value is zero. If each element of a row or column of a determinant multiplied by k, then its value is multiplied by k. If two rows or columns of determinant are proportional, the value of the determinant is zero. A square A = [a i j ]..

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 ..

Consider the GP a, ar, ar 2 ... ..

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

Sum to infinity exists only when r is numerically less than 1. i.e. |r|<..

i) The series formed by the reciprocals of the terms of a geometric series is also a geometric series. ii) There is no general method of finding the sum of a harmonic progressi..

i) A sequence of multiples of 5 5, 10, 15, 20, ii) A sequence of reciprocals of positive integers The above two sequences are clearly the infinite sequence..

A set of numbers arranged in a definite order according to some definite rule is called a sequence. A sequence is a function whose domain is the set N of natural numbers. Indicated sum of the terms in a sequence is called a series. The result of performing the additions is the..

Arrangement and selection of objects are the central ideas of this chapter on permutations and combinations. They are widely applied in solving problems of probability, genetic engineering and life scienc..

1. To find the sum of first n natural numbers. ..