assumed mean in discrete 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 } is a se..

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. ..

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..

If three quantities are in harmonic progression, then the middle quantity is called the harmonic mean between the other tw..

If a, x, b are in A.P, then x is called the arithmetic mean (A.M.) between the extremes a and ..

1. If a, x, b are in A.P, then x is called the arithmetic mean (A.M.) between the extremes a and b. 2. a. To insert n arithmetic means between two given quantities. Let a and b be any two given quantities, and let A 1 ,A 2 ,A 3 ,-----A n be n arithmetic means to be ins..

Let a and b be two given quantities. It is required to insert n harmonic means h 1 , h 2 , h 3 ,....h n between the quantities a and ..