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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 : ..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..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..
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..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..
Count the number of odd numbers.
Count the number of odd numbers. => 6 or 10 or 5 or 4..
Count the number of odd numbers.
Count the number of odd numbers. => 10 or 5 or 4 or 6..
How many odd numbers are there in the figure?
How many odd numbers are there in the figure? => one or four or three or zero..
Choose an odd number.
Choose an odd number. => 17 or 26 or 72 or 18..
Result
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