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| Some Applications of Binomial Theorem for Fractional Index |
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If x be numerically so small that its cube and higher powers may be x3, x4, x5, …. are all approximately zero. |
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If x be numerically so small that its square and higher powers may be neglected, then (1+x)n= 1+nx (approximately), because x2, x3, x4,…. are all approximately zero. |
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| Example: |
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| If x be numerically so small that its cube and higher powers may be neglected, then find the binomial expansions for: |
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| i) (1 + 2x)-4 |
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| Suggested answer: |
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| i) (1 + 2x)-4 |
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