n natural numbers

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 su..

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

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 =..

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

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 indu..

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 image a(n) or..

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. Indicated sum of the terms in a sequence is called a series. The result of p..

For any natural number n, prove tha..

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..

For any rational number n, We accept this expansion without proof. The restriction on x is not required when n is a natural number. Now, we shall see that when n is a natural number, then the above expansion coincides w..