Mathematics Pure WMA11: Binomial expansion Topical Past Paper Questions

Given that the binomial expansion of $(1 + ax)^{n}$, in ascending powers of $x$, is $$ 1-4x+\frac{24}{5}x^{2}+px^{3}+\ldots $$ where $a$, $n$ and $p$ are constants, الجزء $n$. (5) Hence (b) find the value of $p$, (2) (c) state the set of values of $x$ for which the expansion is v…

(a) Find, in ascending powers of x, the first three non-zero terms of the binomial series expansion of $$ \frac{1}{\sqrt{4+x}} $$ giving each coefficient as a simplified fraction. (4) Using the expansion from part (a), (b) state the first three non-zero terms of the binomial seri…

$$ \mathrm{f}(x)=(8-3x)^{\frac{4}{3}}\quad0 (4) (b) Use proof by contradiction to prove that the curve with equation $$ y=8+8x-\frac{15}{2}x^{2} $$ does not intersect the curve with equation $$ y=A-8x+\frac{x^{2}}{2}+Bx^{3}\quad0 (4)