P1035 [NOIP 2002 Junior] Series Summation

Given: $S_n= 1+\dfrac{1}{2}+\dfrac{1}{3}+…+\dfrac{1}{n}$. It is obvious that for any integer $k$, when $n$ is sufficiently large, $S_n>k$. Given an integer $k$, compute the smallest $n$ such that $S_n>k$.

A positive integer $k$.

A positive integer $n$.

【Constraints】 For $100\%$ of the testdata, $1\le k \le 15$. 【Source】 NOIP 2002 Junior, Problem 1. Translated by ChatGPT 5