Composite number
It has factors other than one and itself, e.g., 21 is a composite number..
Composition of ratios
Compounded ratio - If two or more ratios are multiplied term-wise, the ratio thus formed is called their compounded rati..
Case 2: n is odd.
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 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 : ..Question 2
Question: Define an odd number. Answer: A number when divided by 2 gives remainder 1 is called an odd number..
Note 4:
The last term in L.H.S of (ii) and (iii)will depend on the fact as to whether n is 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..
Rational and Irrational Numbers
Introduction - The sets of numbers which every student must remember are: The set of natural numbers, The set of whole numbers, The set of integers, The set of rational numbers, The set of irrational numbers, Set of Real Numbers, Consecuti..
Introduction
The sets of numbers which every student must remember are: The set of natural numbers, The set of whole numbers, The set of integers, The set of rational numbers, The set of irrational numbers, Set of Real Numbers, Consecutive intege..
Note 2:
n C 0 , n C 1 , ..... n C n are called binomial coefficients. n C 0 , n C 2 n C 4 , ..... are called even binomial coefficients. n C 1 , n C 3 , n C 5 .... are called odd binomial coefficient..
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 expressio..
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 expressio..See what our Users say :
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