math series sum


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Series
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. 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..
General Series
1. To find the sum of first n natural numbers. ..
Sequences and Series Examples
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..
Note:
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..
Examples:
1. Find the sum to the series 1+2x+3x 2 +.... to n terms and to infinity when x < ..
Suggested answer:
2. Find the sum to n terms of the series..
Sigma Notation
Sigma Notation - The Greek letter S (read as sigma) denotes the sum. When written before the n t h term of series, implies, the sum of all terms obtained by giving to n the different values 1,2,3n. Thu..
Suggested answer:
4. Method of finding sum of a series whose n t h term is know..
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. ..
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