Question 0810

Find the first three terms of the Maclaurin series for [Your may use standard results given in the List of Formulae (MF26).]

It is given that the first two terms of this series are equal to the first two terms in the series expansion, in ascending powers of ${x,}$ or ${(1 + \frac{25}{2} x)^n.}$ Find ${n}$ and show that the third terms in each of these series are equal.