Finding values in an expansion of the ascending powers of x

Question

If the first three terms in ascending powers of x, in the expansion of (1+(a/x))^n are 1 + 24/x + 252/(x^2), how can I find the values of a and n?

Answer 1

Using the Binomial Theorem, (1 + a/x)ⁿ = (_nC₀)(1)ⁿ(a/x)⁰ + (_nC₁)(1)^n-1(a/x)¹ + (_nC₂)(1)^n-2(a/x)² + ...+ (a/x)ⁿ

= 1 + na/x + (n(n-1)/2)(a²/x²) + ... + (a/x)ⁿ

= 1 + 24/x +252/x² + ... + (a/x)ⁿ

So, an = 24 and a²(n²-n)/2 = 252

Solve for a and n