lim(n→∞)Σ_(k=1)^(n)\(\sqrt{\quad}\)（ｎ＾２－ｋ＾２）
=lim(n→∞)Σ_(k=1)^(n) \(\frac{1}{n}\) ×1/\(\sqrt{\quad}\){（\(n^{2}\)－ｋ＾２）/\(n^{2}\)}
=lim(n→∞)\(\frac{1}{n}\)Σ_(k=1)^(n)1/\(\sqrt{\quad}\){1-(\(\frac{k}{n}\)\()^{2}\)}
=∫_(0)^(1)1/\(\sqrt{\quad}\)(1-\(x^{2}\)) dx
x=sin t とおく
=∫_(0)^(π/2) 1/\(\sqrt{\quad}\)(1-si\(n^{2}\)t) cos t dt
=∫_(0)^(π/2) cos \(\frac{t}{c}\)os t dt
=∫_(0)^(π/2) dt
=π/2