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| Middle Terms for Positive Integral Index |
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| The number of terms in the expansion of (a + b)n depends on the index n. The index n is either even or odd. |
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| Case 1: n is even. |
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| Let n = 2k |
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 The number of terms is n+1 i.e., 2k+1. |
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| The middle term has k terms before it. |
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| Case 2: n is odd. |
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| Let n = 2k+1 |
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 The number of terms is n+1 i.e., (2k + 1) + 1 = 2k + 2. |
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| In this case, there are two middle terms and are after k terms. |
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| Thus, in (a + b)n: |
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| Note: |
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| The middle terms may be easily found out by using the following method: |
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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. |
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ii) When n is odd, we add the odd numbers 1 and 3 to n and divide by
2 to get the middle terms i.e.,  terms. |
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| Example: |
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| Find the middle terms in the expansion of: |
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| Suggested answer: |
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