Part BCSIR NET December 2024normalise-both-sums-before-the-limit

Normalise both sums before the limit

$\lim(n\to\infty) \int_{0}^{1}\int_{0}^{1}\cdots\int_{0}^{1} (x_{1}^{2} + \cdots + x_{n}^{2})/(x_{1} + \cdots + x_{n})$ dx $_{1} \dots$ dx $_{n}$ equals

A.1
B.1/2
C.2
D.2/3✓ Correct

You have the answer. Trap Analysis is why the other three were written.

Not a worked solution repeated four times — the specific reasoning error each wrong option was built to reward, and why this one tests limit assumed to exist.

See pricing

50 are analysed free — try those first.

The trap it tests

Limit assumed to exist

Reasoning with a limit before establishing there is one. limsup is not lim.

Drill statements like this

Normalise both sums before the limit

More on this topic