determine the series obtained by changing the initial value of the infinite series: n ! 2 n + 1 .

Determine the series obtained by changing the initial value of the infinite series: ∑ n=1 ∞ ( - 1 ) n n ! 2 n + 1 . => II or I..

Homologous Series - All organic compounds are made up of a progressively building chain of carbon atoms with a number of compounds having the same functional groups. Such a series of similarly constituted compounds are called a homologous series. Members of a homologou..

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(..

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), ..

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 i..

The equivalent resistance is the sum of the individual resistances connected in series. The above result can be generalised for 'n' number of resistances of different values as R = R1+ R2 +............ + R..

In this chapter, we shall study two series known as the Exponential series and Logarithmic series. In our discussion, we shall make use of mathematical tools like formula for sum of an infinite G.P., combinatorial coefficients, the inequality 2..

The emission of a or b - particles from a radioactive element results in the function of new element called daughter element. If the daughter element still has unstable nucleus, it further disintegrates by emitting a or b - particle and produces a new daughter element. This process of successive di..

2 < e < 3 The value of e rounded off to four decimal places is 2.7183. For complex numbers x,y, we have e x + y = e x y y . For any rational number x, the sum, e x , of the series ..

All members of a homologous series exhibit some common characteristics. They are: All the members of a homologous series can be represented by a common general formula, as they have the same functional group. For example, alkanes can be represented by the formula C n..