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| Particular Terms for Fractional Index |
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| Sometimes, a particular term satisfying certain conditions is required in the binomial expansion of the type (1+x)n. This can be done by expanding (1+x)n to certain terms and then locating the required term. Generally this becomes a tedious task. In such cases, we begin by evaluating the general term Tr+1 and then finding the value of r by assuming Tr+1 to be the required term. |
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| Working rules for finding particular terms: |
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Step 1: In the expansion of (1+x)n, the (r+1)th term is equal to  |
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| Step 2: Find the general terms Tr+1 in the expansion of (1+x)n. |
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| Step 3: Assume that Tr+1 is the desired particular term. |
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| Step 4: Find the value of r. |
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| Step 5: Put the value of r in the term Tr+1. This gives the required particular term(s). |
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| Example: |
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| Suggested answer: |
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| Tr+1 in the expansion of |
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| Putting r = 8, we get coefficient of |
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| Putting r = 9, we get coefficient of |
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