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IB DP Maths: AA HL復(fù)習(xí)筆記1.6.2 Extension of The Binomial Theorem

Category: IB課程, 教材筆記, 福利干貨 Date: 2022年7月11日 下午3:15

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
  • 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.

1-6-2-ib-hl-aa-ext-bin-theorem-we-a

b)? ? ?State the interval of convergence for the complete expansion.

1-6-2-ib-hl-aa-ext-bin-theorem-we-b

 

1-6-2-ib-hl-aa-ext-bin-theorem-we-c

 

 

 

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