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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.
In this case we are going to consider differential equations in the form, y ′ + p ( x ) y = q ( x ) y n Here p(x) and q(x) are continuous functions in the
Correlation and Regression CORRELATION is an important statistical concept which refers to association or interrelationship among variables. The reasons of studying correla
INTRODUCTION : All of us have encountered mathematics while growing up. Some of us have grown to like it, and therefore, enjoy. doing it. Some others have developed a lukewarm rel
what is the graph of 2 sin x
Analysis of questionnaire completed by holiday makers showed that 0.75 classified their holiday as excellent at Malindi. The probability of hot weather in the resort is 0.6. If th
Series - The Basics That topic is infinite series. So just define what is an infinite series? Well, let's start with a sequence {a n } ∞ n=1 (note the n=1 is for convenie
Find all the local maximum and minimum values and saddle points of the function f(x, y) = x 2 - xy + y 2 + 9x - 6y + 10
(3+2)^2+1-3^2.5
a car comes to a stop from a speed of 30m/s in a distance of 804m. The driver brakes so as to produce a decelration of 1/2m per sec sqaured to begin withand then brakes harder to p
A body is constrained to move in a path y = 1+ x^2 and its motion is resisted by friction. The co-efficient of friction is 0.3. The body is acted on by a force F directed towards t
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