Calculating Pi (Formula by a Japanese Mathematician)

Matsunaga Yoshisuke, an Edo-period mathematician, calculated pi to 52 digits in Hōen Sankei, published in 1739.
Other calculations include Seki Takakazu (11 digits, published in 1712) and Takebe Katahiro (41 digits, 1722).

Matsunaga Yoshisuke’s formula for pi　　　　　　　 

\(\normalsize \\ \hspace{20px}{\large\frac{\pi}{3}}=1+{\large\frac{1^2}{4\cdot6}}+{\large\frac{1^2 3^2}{4\cdot6\cdot8\cdot10}}+{\large\frac{1^2 3^2 5^2}{4\cdot6\cdot8\cdot10\cdot12\cdot14}}+\cdot\cdot\cdot\\ \)

Takebe Katahiro’s formula for pi　　　　　　　 

\(\normalsize \\ \hspace{20px}{\large\frac{\pi^2}{9}}=1+{\large\frac{1^2}{3\cdot4}}+{\large\frac{1^2 2^2}{3\cdot4\cdot5\cdot6}}+{\large\frac{1^2 2^2 3^2}{3\cdot4\cdot5\cdot6\cdot7\cdot8}}+\cdot\cdot\cdot\\ \)