Leonhard Euler · 1748 · Internet Archive
Introductio in analysin infinitorum
All 320 leaves · leaf 165
Transcription
IN DEFINIEND. SUMMIS SERIER. INFINIT. 137
Hæ autem summæ P, Q, R, S, &c. ita se habebunt CAP. X.
$P = A = \frac{\pi}{2nk} = \frac{1 \pi}{2nk}$
$Q = \frac{(kk+1)\pi\pi}{4nnkk} = \frac{(2+2kk)\pi^2}{2 \cdot 4 n^2 k^2}$
$R = \frac{(kk+1)\pi^3}{8n^3k^3} = \frac{(6+6kk)\pi^3}{2 \cdot 4 \cdot 6 n^3 k^3}$
$S = \frac{(k^4+4kk+3)\pi^4}{48n^4k^4} = \frac{(24+32kk+8k^4)\pi^4}{2 \cdot 4 \cdot 6 \cdot 8 n^4 k^4}$
$T = \frac{(2k^4+5kk+3)\pi^5}{96n^5k^5} = \frac{(120+200kk+80k^4)\pi^5}{2 \cdot 4 \cdot 6 \cdot 8 \cdot 10 n^5 k^5}$
$V = \frac{(2k^6+
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