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Natural Numbers
The countable numbers are called Natural Numbers. Therefore 1 is the smallest or least of all natural numbers. The highest natural number cannot be said because Natural numbers are infinite. The se..
Step 2:
Assume the validity of the result for n equal to some arbitrary but fixed natural number, say, ..
General Series
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..
Rational and Irrational Numbers
Introduction - The sets of numbers which every student must remember are: The set of natural numbers, The set of whole numbers, The set of integers, The set of rational numbers, The set of irrational numbers, Set of Real Numbers,..
Mathematical Induction Summary
Summary - A sentence is called a statement if it can be adjudged as true or false. Every statement is a sentence, but a sentence may or may not be a statement. A statement involving natural number n is generally denoted by P(n). Principle of mathematical induction states that if..
Conclusion
Let n N and P(n) denote a certain statement or formula or theorem. Then P(n) holds good for every natural number n if (i) it holds for n = 1 and (ii) it holds for n = k+1 whenever it holds for n =..
Mathematical Induction Conclusion
Conclusion - Let n N and P(n) denote a certain statement or formula or theorem. Then P(n) holds good for every natural number n if (i) it holds for n = 1 and (ii) it holds for n = k+1 whenever it holds for n =..
Rational and Irrational Numbers Introduction
Introduction - The sets of numbers which every student must remember are: The set of natural numbers N = {1, 2, 3, 4, 5, } The set of whole numbers W = {0, 1, 2, 3, 4, 5,} The set of integers Z = I = {, -3, -2, -1, 0, 1, 2, 3,} The set of rational number..
Introduction - The sets of numbers which every student must remember are: The set of natural numbers N = {1, 2, 3, 4, 5, } The set of whole numbers W = {0, 1, 2, 3, 4, 5,} The set of integers Z = I = {, -3, -2, -1, 0, 1, 2, 3,} The set of rational number..Sequences and Series
Sequence : A set of numbers arranged in a definite order according to some definite rule is called a sequence.A sequence is a function whose domain is the set N of natural numbers. Series : Indicated sum of the terms in a sequence is called a series. Th..
Summary
1. A sentence is called a statement if it can be adjudged as true or false. 2. Every statement is a sentence, but a sentence may or may not be a statement. 3. A statement involving natural number n is generally denoted by P(n..
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