ISC (Arts) Class 11CISCE
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# General and Middle Terms

#### notes

1.In the binomial expansion for (a + b)^n, we observe that the first term is "^nC_0  a^n, the second term is "^nC_1a^(n–1)b, the third term is "^nC_2 a^(n–2) b^2, and so on. Looking at the pattern of the successive terms we can say that the (r + 1)^(th)term is "^nC_ra^(n–r)b^r. The (r + 1)^th term is also called the general term of the expansion (a + b)^n. It is denoted by T_(r+1) Thus T_(r+1) = "^nC_r a^(n–r)b^r.

2. Regarding the middle term in the expansion (a + b)n, we have
(i) If n is even, then the number of terms in the expansion will be n + 1. Since n is even so n + 1 is odd. Therefore, the middle term is ((n + 1 + 1)/2)^(th) , i.e., (n/2+1)^(th) term.
(ii) If n is odd, then n +1 is even, so there will be two middle terms in the expansion, namely ((n+1)/2)^(th) term and ((n+1)/2 + 1) term.
(ii) If n is odd, then n +1 is even, so there will be two middle terms in the expansion, namely ((n+1)/2)^(th) term and ((n+1)/2 + 1) term.

3. In the expansion of (x +1/x)^(2n) ,  where x  ≠ 0, the middle term is ((2n +1 +1)/2)^(th), i.e., (n + 1)^(th) term, as 2n is even.

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General and Middle Terms [00:06:42]
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