Question Type 9: Using binomial theorem for fractional indices Exercises

Use the first three nonzero terms of the expansion of $(1-x)^{\tfrac{1}{3}}$ to approximate $(0.96)^{\tfrac{1}{3}}$, 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 $(1 - 3x)^{\tfrac12}$ in ascending powers of $x$ up to and including the term in $x^3$.

Expand $(1+x)^{\tfrac{5}{2}}$ 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 $x^2$.