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..
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..
Sequences and Series
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 ima..
Step 4:
Conclude that the result holds for all natural numbers..
Step I:
Denote the statement involving natural numbers n = 1, 2,. by P(n..
Whole numbers
The set of whole numbers is the set of natural numbers along with zero. so W = the set of whole numbers = 0,1,2,3,............ so Zero is the least number of the set of Whole numbers. As the whole numbers is an infinite set..
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 i..
Using Principle of Mathematical Induction
For any natural number n, prove tha..
For any natural number n, prove tha..General Series
1. To find the sum of first n natural numbers. ..
1. To find the sum of first n natural numbers. ..General Series
General Series - 1. To find the sum of first n natural numbers. ..
General Series - 1. To find the sum of first n natural numbers. .. Result
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