实测下来提升很大，一些比较困难综合的高等数学问题也能做对。 
Q1: 
\lim_{n\to\infty} \sum_{k=1}^n (1-\frac{k}{n})\ln(1+\frac{k}{n^2}) = \underline{\qquad\qquad}. 
A: 
To find the limit as ( n ) approaches infinity of the sum ( \sum_{k=1}^n \left(1 - \frac{k}{n}\right) \ln\left(1 + \frac{k}{n^2}\right) ), we start by approximating the logarithm using its Taylor series expansion. For small ( x ), ( \ln(1 + x) \approx x - \frac{x^...