Past exam of the mathematics course of the University of Cambridge / 2016 / ia / Paper 1 / 11D / a

Use rationalization of a square-root difference to avoid subtracting two large, nearly equal quantities:Since $1/n\to 0$ and the square root is continuous at $1$, the denominator tends to $2$. The reciprocal limit law established above is applicable because this limit is nonzero. HenceThe limit is one half; rationalization exposes the finite difference hidden by cancellation.