カテゴリー: 総和総乗問題

\[ \frac{1}{1}+\frac{1}{1+2}+\frac{1}{1+2+3}+\frac{1}{1+2+3+4}+\cdots=? \]

\[ \sum_{k=0}^{\infty}C\left(3n,3k\right)=? \]

\[ \frac{1}{\sqrt{5}+\sqrt{6}}+\frac{1}{\sqrt{6}+\sqrt{7}}+\cdots+\frac{1}{\sqrt{28}+\sqrt{29}}+\frac{1}{\sqrt{29}+\sqrt{30}}=? \]

\[ \sum_{k=0}^{n}kC^{2}\left(n,k\right)=? \]

\[ \sum_{k=0}^{n}\frac{k!}{k!+\left(n-k\right)!}=? \]

\[ \lim_{n\rightarrow\infty}\prod_{k=1}^{n}\left(1+\frac{k}{n^{2}}\right)=? \]

\[ \frac{3}{1!+2!+3!}+\frac{4}{2!+3!+4!}+\frac{5}{3!+4!+5!}+\cdots+\frac{100}{98!+99!+100!}=? \]