<ol class="abc-list"><li><div class="list-item-paragraph">Using the standard series expansion, expand \(\ln(1+\sin x)\) where&nbsp;\(0 \le x &lt; \pi\), in ascending powers of \(x\), up to and including the term in \(x^3\).<span class="inline-marks">[3]</span></div></li><li><div class="list-item-paragraph">The first two terms of the series in part (a) are equal to the first two terms in the series expansion of \(\frac{ax}{(1+bx)^2}\), where&nbsp;\(a\) and \(b\) are non-zero constants. Find the values of \(a\) and \(b\). Hence write down the third term in the series expansion of \(\frac{ax}{(1+bx)^2}\).<span class="inline-marks">[4]</span></div></li></ol>

Using the standard series expansion, expand \(\ln(1+\sin x)\) where \(0 \le x < \pi\), in ascending powers of \(x\), up to and including the term in \(x^3\).

The first two terms of the series in part (a) are equal to the first two terms in the series expansion of \(\frac{ax}{(1+bx)^2}\), where \(a\) and \(b\) are non-zero constants. Find the values of \(a\) and \(b\). Hence write down the third term in the series expansion of \(\frac{ax}{(1+bx)^2}\).

2024 MI PRU2 P1 Q4

2024 MI PRU2 P1 Q4