math infinite series

Summary - (i) Let X be a set of numbers and f : N n X be a function, then the ordered set {f(1), f(2),...., f(n)} is called a finite sequence in X. (ii) Let X be a set of numbers and f : N X be a function, then the ordered set {f(1), f(2),....} is called an infinite sequence in X. If {T n..

Indicated sum of the terms in a sequence is called a series. The result of performing the additions is the sum of the series...

General Series - 1. To find the sum of first n natural numbers. ..

1. To find the sum of first n natural numbers. 2. To find the sum to squares of first n natural numbers. 3. To find the sum to the cubes of first n natural numbers. 4. Method of finding sum of a series whose nth term is know..

Introduction - A set of numbers arranged in a definite order according to some definite rule is called a sequenc..

A series of the form a + (a + d)r + (a + 2d)r 2 + ... is called an Arithmetic-Geometric series. In the series if we put d = 0 we get GP and if we put r = 1, we get an A..

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) 1 + 4 + 7 + 10 + ... is a series in which first term is 1, second term is 4, third term is 7 and so on. ii) 3 - 9 + 27 - 81 + ... is also a series in which the first term is 3, second term is -9, third term is 27 and so ..

1. Find the sum to the series 1+2x+3x 2 +.... to n terms and to infinity when x < ..

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..