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| Particular Terms for Positive Integral Index |
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| Sometimes, a particular term satisfying certain conditions is required in the binomial expansion of the type (a + b)n. This can be done by expanding (a + b)n and then locating the required term. Generally this becomes a tedious task, specially when the index n is large. 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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| To get the term independent of x, we put the power of x equal to zero and get the value of r for which the term is independent of x. Putting this value of r in Tr+1, we get the term independent of x. |
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| Working rules for finding particular terms: |
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| Step 1: Find the general term Tr+1 in the expansion of (a + b)n. |
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| Step 2: Assume that Tr+1 is the desired particular term. |
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| Step 3: Find the value of r. |
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| Step 4: 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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| Find the coefficient of x40 in the expansion of (1 + 2x + x2)27 . |
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| Suggested answer: |
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| Let Tr+1 be the term containing x40. |
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| \ r = 40 |
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