Question Type 9: Using binomial theorem for fractional indices Bootcamps

Expand $(1 - 3x)^{\tfrac12}$ in ascending powers of $x$ up to and including the term in $x^3$.

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

Expand $(4 + 3x)^{\tfrac12}$ in ascending powers of $x$ up to and including the term in $x^2$.

Expand $(1 + 2x)^{-\tfrac12}$ in ascending powers of $x$ up to and including the term in $x^3$.

Use the first three nonzero terms of the expansion of $(1-x)^{\tfrac13}$ to approximate $(0.96)^{\tfrac13}$, giving your answer to 4 decimal places.

Expand $(9 - 4x)^{-\tfrac12}$ in ascending powers of $x$ up to and including the term in $x^2$.

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

State the general term in the binomial expansion of $(1+x)^{\tfrac12}$ and write $T_{4}$ (the term in $x^3$).

Expand $(2 - x)^{-\tfrac32}$ in ascending powers of $x$ up to and including the term in $x^2$.