Leonhard Euler · 1748 · Internet Archive
Introductio in analysin infinitorum
All 320 leaves · leaf 256
Transcription
228 DE SERIEBUS. EX
LIB. I.
denique vero erit
$ \frac{MM}{N} = \frac{2^n+1}{2^n-1} \cdot \frac{3^n+1}{3^n-1} \cdot \frac{5^n+1}{5^n-1} \cdot \frac{7^n+1}{7^n-1} \cdot \frac{11^n+1}{11^n-1} \cdot \&c. $
Ex cognitis ergo $M$ & $N$, praeter valores horum productorum, summae harum Serierum habebuntur
$ \frac{1}{M} = 1 - \frac{1}{2^n} - \frac{1}{3^n} - \frac{1}{5^n} + \frac{1}{6^n} - \frac{1}{7^n} + \frac{1}{10^n} - \frac{1}{11^n} \&c. $
$ \frac{1}{N} = 1 - \frac{1}{2^{2n}} - \frac{1}{3^{2n}} - \frac{1}{5^{2n}} + \frac{1}{6^{2n}} - \frac{1}{7^{2n}} + \frac{1}{10^{2n}} - \frac{1}{
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