IB DP Maths: AA HL復(fù)習(xí)筆記1.6.2 Extension of The Binomial Theorem
How do I use the binomial theorem for fractional and negative indices?
How do we use the binomial theorem to estimate a value?
- The binomial expansion can be used to form an approximation for a value raised to a power
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- Check that the value of?x?is within the?interval of convergence?for the expression
- If?x?is outside the interval of convergence then the approximation may not be valid
Exam Tip
- Students often struggle with the extension of the binomial theorem questions in the exam, however the formula is given in the formula booklet
- Make sure you can locate the formula easily and practice substituting values in
- Mistakes are often made with negative numbers or by forgetting to use brackets properly
- Writing one term per line can help with both of these
Worked Example
a)? ? ?Write down the first three terms.
b)? ? ?State the interval of convergence for the complete expansion.
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