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
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