Steps / Historical AI

Leonhard Euler · 1748 · Internet Archive

Introductio in analysin infinitorum

All 320 leaves · leaf 158

Transcription

130 DE USU FACTORUM INVENTORUM LIB. I. $(1+\frac{1}{25})$ &c.. Facta ergo applicatione superioris regulæ ad hunc casum, erit $A=\frac{\pi\pi}{6}$; $B=\frac{\pi^4}{120}$; $C=\frac{\pi^6}{5040}$; $D=\frac{\pi^8}{362880}$ &c.. Quod si ergo ponatur $P=1+\frac{1}{4}+\frac{1}{9}+\frac{1}{16}+\frac{1}{25}+\frac{1}{36}+\&c.$ $Q=1+\frac{1}{4^2}+\frac{1}{9^2}+\frac{1}{16^2}+\frac{1}{25^2}+\frac{1}{36^2}+\&c.$ $R=1+\frac{1}{4^3}+\frac{1}{9^3}+\frac{1}{16^3}+\frac{1}{25^3}+\frac{1}{36^3}+\&c.$ $S=1+\frac{1}{4^4}+\frac{1}{9^4}+\frac{1}{16^4}+\frac{1}{25^4}+\frac{1}{36^4}+\&c.$ $T=1+\frac{1}{4^ [TRUNCATED]
confidence 0.25 9 expressions source scan at the Internet Archive

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