Summary
of (a + b) n and is given by - If n is an odd natural number, then there are two middle terms in the expansion of (a + b)n and are given by i) The sum of all binomial coefficients in the expansion of (1+x) n is 2 n . ii) The sum of all even binomial coefficients in the..
of (a + b) n and is given by - If n is an odd natural number, then there are two middle terms in the expansion of (a + b)n and are given by i) The sum of all binomial coefficients in the expansion of (1+x) n is 2 n . ii) The sum of all even binomial coefficients in the..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..
Middle Terms for Positive Integral Index
The number of terms in the expansion of (a + b) n depends on the index n. The index n is either even or odd..
Middle Terms for Positive Integral Index
Middle Terms for Positive Integral Index - The number of terms in the expansion of (a + b) n depends on the index n. The index n is either even or odd..
Middle Terms for Positive Integral Index
The number of terms in the expansion of (a + b) n depends on the index n. The index n is either even or odd..
Note:
The middle terms may be easily found out by using the following method: i) When n is even, we add the even number 2 to n and divide by 2 to get the middle term i.e., term. ii) When n is odd, we add the odd numbers 1 and 3 to n and divide by 2 to get the mi..
The middle terms may be easily found out by using the following method: i) When n is even, we add the even number 2 to n and divide by 2 to get the middle term i.e., term. ii) When n is odd, we add the odd numbers 1 and 3 to n and divide by 2 to get the mi..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..
Study the following examples
1. The numbers 2, 3, 5 and 8. 2. The solutions of the equation x 2 - 2x - 15 = 0. 3. The letters of the word "Chase". 4. People living in our locality. 5. The students Mary, Hillary, Catherine. 6. The workers who are absent from the factory. 7. The capital cities of Asia. 8. The positiv..
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..
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