conclusion sequence and series

A compound proposition is a tautology if it is always true for all possible combination of the truth values of its components. If a compound proposition which is always false for all possible combination of the truth values, of its components then it is called a contradiction. Consider two compound..

.com/content/math/discrete-math/permutations-and-combinations/permutations-and-combinationsindex.php' title='Permutations and Combinations'>Permutations and Combinations Permutations : The different arrangements that can be made with a given number of things taking some or all of them at a time are..

Ecological Succession - "The occurrence of relatively definite sequence of communities over a long period of time in the same area resulting in establishment of stable or climax community, is known as ecological or biotic succession". The first community which is inhabiting the area will ..

Introduction - The word 'Induction' means method of reasoning from individual cases to general ones or from observed instances to unobserved ones. Many important mathematical formulae are such that a result is formed by some means which does not provide for a direct proof. Mathematical Induction is..

All the events which change a zygote into a fully developed organism is called embryonic development. The entire process of development is called embryogenesis. Von Bear is called the "Father of Modern Embryology". Embryonic Development includes a definite series of fundamentally similar ..

Linear equations/inequalities Monomials and polynomials Factoring second and third degree polynomials Rational expressions/functions Quadratic equations Quadratic functions Exponents, factors, variation, exponential growth/decay Hypothesis, counterexamples Correlation for data Patterns, ..

While studying the biotic components in an ecosystem we have realised that food prepared by green plants is consumed by a series of consumers, both herbivores and carnivores, and finally broken down into their elements and released back into nature by decomposers in nature. The nutritiona..

Food Chains and Food Webs - While studying the biotic components in an ecosystem we have realised that food prepared by green plants is consumed by a series of consumers, both herbivores and carnivores, and finally broken down into their elements and released back into nature by decompose..

Summary - All these evidences point to the fact that evolution occurs. The exact mechanism of evolution, however, is not yet conclusively proven. But constant study and research in the above fields is continuing for answers. Asexual reproduction results in identical offspring whereas sexu..

Limits- operations on functions Continuity of a function Intermediate value, extreme value theorem Derivatives, differentiability Derivatives of functions Chain rule Rolle's theorem, mean value theorem, and L'Hopital's rule Maxima, minima, inflection points, intervals Newton's method (app..