<ol class="abc-list"><li data-list-item-id="item-a"><div class="list-item-paragraph">The expansion of \((1+kx)^n\) in ascending powers of \(x\) is \(1+\frac{7}{3}x+\frac{7}{3}x^2+\ldots\).<br>Show that&nbsp;\(k=\frac{1}{3}\) and calculate the value of \(n\).<span class="inline-marks">[4]</span></div></li><li data-list-item-id="item-b"><div class="list-item-paragraph">Explain why all terms in the expansion of \(\left(px^2-\frac{1}{x^4}\right)^{12}\) contain only even powers of \(x\).<span class="inline-marks">[4]</span></div></li></ol>

The expansion of \((1+kx)^n\) in ascending powers of \(x\) is \(1+\frac{7}{3}x+\frac{7}{3}x^2+\ldots\).
Show that \(k=\frac{1}{3}\) and calculate the value of \(n\).

Explain why all terms in the expansion of \(\left(px^2-\frac{1}{x^4}\right)^{12}\) contain only even powers of \(x\).

Binomial Theorem

Binomial Theorem