ENG1005 MUM S2 2025 Applied class quiz week 11 (Total mark for all 12 weeks of applied quizzes is 5%)

Question text What is the limit of the sequence \(a_n = {\frac{5^{n}+5\,n^2+2\,n}{5^{n+2}-n^2-5\,n}}\) as \(n \to \infty\)? You may use that fact that exponential growth is faster than any polynomial ...