IB Mathematics Analysis and Approaches Question Type 9: Using Binomial Theorem for Fractional Indices Exercises

Use the first three nonzero terms of the expansion of $(1-x{)}^{\frac{1}{3}}$ to approximate $(0.96{)}^{\frac{1}{3}}$, giving your answer to 4 decimal places.

Use the binomial series to approximate $\sqrt{1.1}$, giving your answer to 4 decimal places.

Expand $(4+3x{)}^{\frac{1}{2}}$ in ascending powers of $x$ up to and including the term in $x^2$.

State the general term in the binomial expansion of $(1+x{)}^{\frac{1}{2}}$ and write $T_4$ (the term in $x^3$).

Expand $(9-4x{)}^{-\frac{1}{2}}$ in ascending powers of $x$ up to and including the term in $x^2$.

Expand $(1-3x{)}^{\frac{1}{2}}$ in ascending powers of $x$ up to and including the term in $x^3$.

Expand $(1+x{)}^{\frac{5}{2}}$ in ascending powers of $x$ up to and including the term in $x^3$.

Expand $(1+2x{)}^{-\frac{1}{2}}$ in ascending powers of $x$ up to and including the term in $x^3$.

Expand $(2-x{)}^{-\frac{3}{2}}$ in ascending powers of $x$ up to and including the term in $x^2$.