sum of odd natural numbers

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..

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 ..

General Series - 1. To find the sum of first n natural numbers. ..

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..

3. To find the sum to the cubes of first n natural numbers. ..

Let n = 2k+1 The number of terms is n+1 i.e., (2k + 1) + 1 = 2k + 2. In this case, there are two middle terms and are after k terms. Thus, in (a + b) n : ..

Let a = First term, r = common ratio, n = number of terms. Multiply both sides of (i) by r, the common ratio. Subtracting (ii) from (i), we get ..

Consider the GP a, ar, ar 2 ... ..

Question: Define an odd number. Answer: A number when divided by 2 gives remainder 1 is called an odd number..

The last term in L.H.S of (ii) and (iii)will depend on the fact as to whether n is even or odd..