# Solved Examples based on Progression Part 1

May 19th, 2015
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Example 1: Find the sum of the series 1 – 3 + 5 – 7 + 9 – 11 + …… upto n terms. Solution : This problem can be solved by different approachesm of course some one is tricky, some one is little bit lengthy. Now you have to judge which one is suitable for your.

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GRAPHSGraphs and DigraphsGraph theory is one important aspect in Discrete mathematics. Graphs in this sense have nothing to do with the graphs of functions y = f(x) in the xy coordinate plane. Graphs were first introduced in the eighteenth century.The graphs we are concerned with are like road maps, circuit diagrams of flowcharts in the sense that they depict connections or relationships between various parts of the diagram.Graph theory is the study of directed and undirected graphs. A picture of a graph or diagram consisting of points corresponding to number of V(G), set of vertices, and line segment or arrow corresponding to numbers of E(G).This section aims to:1. Define and diagram the basic terms of graphs and digraph; and2. Discuss the application of graphs.A graph denoted by G = (V, E) consists of a finite set V, called the set of vertices (points or nodes) and a set E of unordered pairs of distinct vertices, called the set of edges.If e = {u, v} is an edge of G, we say that e joins u and v and e is incident to u and to v.Illustration. A picture of the graph with set { a, b, c, d, e} and edge set {ab, ac, cb, ad} or {e1, e2, e3, e4}. Edge e1 = {ab} joins a and b which are the endpoints. Vertex f, an isolated point is incident to no edges. See fig. 7.1.1 Note that a graph is sometimes defined as a simple undirected graph. Synonyms for vertex is point and for edge is arc or line.A directed graph of simply digraph G = (

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