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..

Conclude that the result holds for all natural numbers..

Assume the validity of the result for n equal to some arbitrary but fixed natural number, say, ..

Denote the statement involving natural numbers n = 1, 2,. by P(n..

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..

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..

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..

For any natural number n, prove tha..

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 =..

1. To find the sum of first n natural numbers. ..