# Using familiar lemma

Calculus Level 4

Let $$\displaystyle L= \lim_{n\to\infty} \sum_{k=1}^n \dfrac{1}{n+\pi(k)\ln n},$$ where $$\pi(k)$$ denotes the number of primes not exceeding $$k.$$

Find the closed form of $$L$$ and submit your answer as $$\big\lceil 1000L\big\rceil.$$

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