math series mathematics

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..

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, ..

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

4. Method of finding sum of a series whose n t h term is know..

i) 1.2 + 2.4 + 3.8 +.... to n terms The n t h term of (1,2,3,....n) is n. The n t h term of (2,4,8,...) is The n t h term of the given series is n2 n Subtracting (ii) from (i), we have ..

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. ..