Past exam of the mathematics course of the University of Cambridge / 2024 / ia / Paper 4 / 7E / a / ii / Solution

LetFor $n\ge 3$, the binomial theorem givesConsequently $(1000n^2+4)/1.1^n\to 0$: given $\epsilon >0$, the displayed rational upper bound is below $\epsilon$ for all sufficiently large $n$. Thus, directly from the definition of convergence,