Steps / Historical AI

Leonhard Euler · 1748 · Internet Archive

Introductio in analysin infinitorum

All 320 leaves · leaf 178

Transcription

150 DE ALIIS ARCUUM ATQUE LIB. I. $l\pi = l4 \{$ $-\frac{1}{9} - \frac{1}{2 \cdot 9^2} - \frac{1}{3 \cdot 9^3} - \frac{1}{4 \cdot 9^4} - \&c.$ $-\frac{1}{25} - \frac{1}{2 \cdot 25^2} - \frac{1}{3 \cdot 25^3} - \frac{1}{4 \cdot 25^4} - \&c.$ $-\frac{1}{49} - \frac{1}{2 \cdot 49^2} - \frac{1}{3 \cdot 49^3} - \frac{1}{4 \cdot 49^4} - \&c.$ $\&c.$ In his Seriebus numero infinitis verticaliter descendendo ejusmodi prodeunt Series, quarum summas supra jam invenimus, quare si brevitatis gratia ponamus $A = 1 + \frac{1}{3^2} + \frac{1}{5^2} + \frac{1}{7^2} + \frac{1}{9^2} + \&c.$ $B = 1 + \frac{1}{3^4} + \frac{1}{5^4} + \frac{1 [TRUNCATED]
confidence 0.79 6 expressions source scan at the Internet Archive

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