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We will look at three types of progressions called Arithmetic, Geometric and Harmonic Progression. Before we start looking at the intricacies of these let us understand what is meant by series. A series is a collection of numbers which may or may not terminate at some point. The first set of series that terminate is called finite series and the second one that do not terminate is called infinite series. In the theoretical sense an infinite series conveys that the number of elements in the series are so large that it is practically uncountable. Generally, series are expressed in an abridged form in terms of a general term known as nth term. Therefore, given a series we can obtain its nth term or else given an nth term we can obtain the different elements of that series. For example, consider a simple nth term which is:
If we substitute n = 1, the value of Tn=1 will be
If we substitute n = 2, the value of Tn=2 will be
If we continue to substitute different values for n, like we did above, we get different values of this particular series. This is an example of infinite series, whereas a series like 1, 2, 3, 4, 5, 6 is an example of finite series. The general term is given by Tn = n + 1, where n takes values from 0 to 5. After looking at these two examples we find that a series is finite or infinite depending on the values taken by n. In other words, a series terminates depending on the extent of values taken by n.
Characteristics of Time Series Time series has the given characteristics. a) A long term trend (T) -tendency of the whole series to fall and rise. b) Seasonal variati
Squeeze Theorem (Sandwich Theorem and the Pinching Theorem) Assume that for all x on [a, b] (except possibly at x = c ) we have, f ( x )≤ h (
Describe Adding and Subtracting Fractions in details? To add or subtract fractions, here are some steps: 1. Find the lowest common denominator (LCD) or any common denominato
what is the least number of faces and bases the paperweight could have?
Given the hypotenuse of a right triangle: Given that the hypotenuse of a right triangle is 18" and the length of one side is 11", what is the length of another side? a 2 +
1. A rectangular piece of cardboard measuring 15 inches by 24 inches is to be made into a box with an open top by cutting equal size squares from each comer and folding up the side
Define Markov chain Random processes with Markov property which takes separate values, whether t is discrete or continuous, are known as Markov chains.
Short Cuts for solving quadratic equations
similar triangles diagram
Proof of: lim q →0 (cos q -1) / q = 0 We will begin by doing the following, lim q →0 (cosq -1)/q = lim q →0 ((cosq - 1)(cosq + 1))/(q (cosq + 1)) = lim q
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