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File:Mercator series.svg

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Summary

Description
English: Graph showing how the Mercator Series converges to ln(x) for 0 < x ≤ 2 with an increasing number of terms n included in the finite series
Deutsch: Mercator-Reihe für unterschiedliche Werte von n.

Die Grafik zeigt die Graphen der Reihe

wobei n die Werte 1,2, 3 und 10 annimmt zusammen mit dem Graph des natürlichen Logarithmus. Die Reihe konvergiert für x aus dem halboffenen Intervall (0,2] gegen den natürlichen Logarithmus.
Dansk: Graf, som viser hvorledes 'te ordens Taylorpolynomiet
for i angrebspunktet konverger mod den naturlige logaritme for med et stigende antal led i den endelige række. I grænsen er Taylorpolynomiet med substitutionen identisk med Mercators række.
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Source Own work
Author Georg-Johann
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20 August 2010

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Date/TimeThumbnailDimensionsUserComment
current13:36, 31 August 2010Thumbnail for version as of 13:36, 31 August 2010480 × 480 (6 KB)Georg-Johanndickere Schraffur (für bessere Vorschau)
00:17, 21 August 2010Thumbnail for version as of 00:17, 21 August 2010480 × 480 (6 KB)Georg-Johannset encoding to utf-8
20:08, 20 August 2010Thumbnail for version as of 20:08, 20 August 2010480 × 480 (6 KB)Georg-Johann{{Information |Description={{en|1=Mercator series for different values of ''n''.}} {{de|1=Mercator-Reihe für unterschiedliche Werte von ''n''. }} |Source={{own}}: {{handSVG}} |Author=[[User:Georg-Johann|Geor
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