series in math

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

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..

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

Sequence - 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 N under 'a' by a n or t ..

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..

Let a=first term, d = common difference, l=t n =last term, s = required sum. Then, Writing the series in the reverse order, Adding together the two series, ..

Each one of the following series form an A.P. i) 1, 3, 5, 7, ii) 3, 7, 11, 15, iii) 15, 12, 9, iv) x, x - d, x - 2d, ..... The common difference is found by subtracting any term of the series from the immediate succeeding term. In the above example, common difference in th..

2. Find the sum to n terms of the series..

Let the n t h term of series be an 3 + bn 2 + cn + d t n = an 3 + bn 2 + cn + d where a, b, c, d are constants. ..