isi-entrance 2024 Q23

isi-entrance · India · UGA Sequences and Series Limit Evaluation Involving Sequences

The limit $$\lim_{n \rightarrow \infty} \frac{2\log 2 + 3\log 3 + \cdots + n\log n}{n^2 \log n}$$ is equal to
(A) 0
(B) $1/4$
(C) $1/2$
(D) 1

The limit
$$\lim_{n \rightarrow \infty} \frac{2\log 2 + 3\log 3 + \cdots + n\log n}{n^2 \log n}$$
is equal to\\
(A) 0\\
(B) $1/4$\\
(C) $1/2$\\
(D) 1