use the series test to determine whether the series 1 1 2 1 3 1 4 ... is convergent or divergent.

Use the p -Series Test to determine whether the series 1 + 1 2 + 1 3 + 1 4 + ... is convergent or divergent. => convergent or divergent or ..

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 i..

Use the Alternating Series Test to determine whether the series ∑ n=1 ∞ 3 ( - 1 ) n 4 n 2 + 3 n is convergent or divergent. => divergent or neithe..

. Hydrocarbons and their major sub groups form a homologous series of organic compounds. As an illustrative example, the simplest of all hydrocarbons is methane whose molecular formula is CH 4 . This molecule consists of a single carbon atom linked to four hydrogen ato..

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..

Find the next term in the series 1, 1, 2, 4, 7, ___, . . . => 3 or 11 or 2 or 6..

Every one element of A corresponds to one element of B. Every first element has a corresponding second element. One-one relations in examples 1 and 2 are called one-one functions. Every element of set A has one image in set B. ..

Determine whether the series ∑ n=1 ∞ n 2 is convergent or divergent. If it converges, then determine its sum. => cannot be determined or convergent; 1 6 or divergent ..

Use comparison test to determine whether the series ∑ n=1 ∞ 2 n + 3 2 n 4 + 5 n 3 converges or diverges. => converges or diverges or neither ..

Introduction Exponential and Logarithmic Series - 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 infi..