Question 43
For a positive integer $n$, define
$$f(n)=\frac{4n+\sqrt{4n^2-1}}{\sqrt{2n+1}+\sqrt{2n-1}}.$$
Calculate
$$f(1)+f(2)+f(3)+\cdots+f(40).$$
$$f(n)=\frac{4n+\sqrt{4n^2-1}}{\sqrt{2n+1}+\sqrt{2n-1}}.$$
Calculate
$$f(1)+f(2)+f(3)+\cdots+f(40).$$