sequence of positive numbers

>These formulae are used when 'last term' is given. (v) If 'a' and 'r' be the first term and common ratio of a G.P. such (vi) If the sequence a, G 1 , G 2 ,....,G n , b of positive numbers is a G.P., then the numbers G 1 , G 2 ,....,G n , are called the n geo..

1, 3, 5, 7..... (adding 2 to every term) 1, 4, 16, 64 (Multiplying by 4 every term) 20, 17, 14 . (add -3 to every term) The different numbers in a sequence are called terms of sequence. The subscripts denote the position of the term. In the second ex..

The word 'Induction' means method of reasoning from individual cases to general ones or from observed instances to unobserved ones. Many important mathematical formulae are such that a result is formed by some means which does not provide for a direct proof. Mathematical Induction is a principle by..

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..

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 r..

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

A sequence is called finite if the number of terms is finite. A finite sequence has always a last ter..

Middle Terms for Positive Integral Index - The number of terms in the expansion of (a + b) n depends on the index n. The index n is either even or o..

General Term for Positive Integral Index is: For 0 r n, we have T r + 1 = n C r a n - r b r..

Greatest Terms for Positive Integral Index - In (a + b) n , let 'a' and 'b' be both positive numbers. As r increases, the factor decreases. So long as this factor is greater than 1, T r..