Steps / Historical AI

Leonhard Euler · 1748 · Internet Archive

Introductio in analysin infinitorum

All 320 leaves · leaf 161

Transcription

IN DEFINIEND. SUMMIS SERIER. INFINIT. 133 $T = \frac{7936}{1 \cdot 2 \cdot 3 \cdots 9} \frac{\pi^{10}}{2^{11}}$; $V = \frac{353792}{1 \cdot 2 \cdot 3 \cdots 11} \frac{\pi^{12}}{2^{13}}$ $W = \frac{22368256}{1 \cdot 2 \cdot 3 \cdots 13} \frac{\pi^{14}}{2^{15}}$. CAP. X. 170. Eædem summæ Potestatum numerorum imparium inveniri possunt ex summis præcedentibus, in quibus omnes numeri occurrunt; si enim fuerit $M = 1 + \frac{1}{2^n} + \frac{1}{3^n} + \frac{1}{4^n} + \frac{1}{5^n} + \&c.$, erit ubique, per $\frac{1}{2^n}$ multiplicando, $\frac{M}{2^n} = \frac{1}{2^n} + \frac{1}{4^n} + \frac{1}{6^n} + \frac{1}{8^n} + \&c.$, quæ Series numeros tantum pares continens, si a priori subtrahat [TRUNCATED]
confidence 0.95 6 expressions source scan at the Internet Archive

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