Series
http://www.maa.org/taxonomy/term/41618/0
en\( \lim_{m \rightarrow \infty} \sum_{k=0}^{m} (k/m)^m\) \(= e/(e-1) \)
http://www.maa.org/programs/faculty-and-departments/classroom-capsules-and-notes/limm-rightarrow-infty-sumk0m-kmm-ee-1
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p><em>Two proofs, one elementary, of the limit in the title are presented.</em></p>
</div></div></div>Ramanujan, Modular Equations, and Approximations to Pi, or, How to Compute One Billion Digits of Pi
http://www.maa.org/programs/maa-awards/writing-awards/ramanujan-modular-equations-and-approximations-to-pi-or-how-to-compute-one-billion-digits-of-pi
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p class="MsoNormal"><b>Award</b>: Merten Hasse</p>
<p class="MsoNormal"><b>Year of Award:</b> 1993, and also the Chauvenet Prize in 1993</p>
<p class="MsoNormal"><b>Publication Information:</b><i> The American Mathematics Monthly,</i> Vol. 96 (1989), pp. 201-219.</p>
<p class="MsoNormal"><b>Summary:</b> A discussion of Ramanujan’s approach to approximating pi from a modern computational context.</p>
<p class="MsoNormal"><a href="/sites/default/files/pdf/upload_library/22/Hasse/00029890.di991740.99p0456b.pdf" title="Read the Article">Read the Article</a></p></div></div></div>Servois' 1814 Essay on a New Method of Exposition of the Principles of Differential Calculus, with an English Translation - Lagrange's Influence
http://www.maa.org/publications/periodicals/convergence/servois-1814-essay-on-a-new-method-of-exposition-of-the-principles-of-differential-calculus-with-an-5
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even">A study and English translation of Servois' attempt to place calculus on a foundation of algebraic analysis without recourse to infinitesimals, continuing the work of Lagrange.</div></div></div>Servois' 1814 Essay on a New Method of Exposition of the Principles of Differential Calculus, with an English Translation - Lagrange's [i]fonction derivee[/i]
http://www.maa.org/publications/periodicals/convergence/servois-1814-essay-on-a-new-method-of-exposition-of-the-principles-of-differential-calculus-with-an-4
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even">A study and English translation of Servois' attempt to place calculus on a foundation of algebraic analysis without recourse to infinitesimals, continuing the work of Lagrange.</div></div></div>Servois' 1814 Essay on a New Method of Exposition of the Principles of Differential Calculus, with an English Translation - Lagrange and Algebraic Analysis
http://www.maa.org/publications/periodicals/convergence/servois-1814-essay-on-a-new-method-of-exposition-of-the-principles-of-differential-calculus-with-an-3
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even">A study and English translation of Servois' attempt to place calculus on a foundation of algebraic analysis without recourse to infinitesimals, continuing the work of Lagrange.</div></div></div>Servois' 1814 Essay on a New Method of Exposition of the Principles of Differential Calculus, with an English Translation - The Golden Age of Analysis
http://www.maa.org/publications/periodicals/convergence/servois-1814-essay-on-a-new-method-of-exposition-of-the-principles-of-differential-calculus-with-an-2
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even"><p>A study and English translation of Servois' attempt to place calculus on a foundation of algebraic analysis without recourse to infinitesimals, continuing the work of Lagrange.</p>
</div></div></div>Servois' 1814 Essay on a New Method of Exposition of the Principles of Differential Calculus, with an English Translation - Servois and the Foundation for Calculus
http://www.maa.org/publications/periodicals/convergence/servois-1814-essay-on-a-new-method-of-exposition-of-the-principles-of-differential-calculus-with-an-1
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even">A study and English translation of Servois' attempt to place calculus on a foundation of algebraic analysis without recourse to infinitesimals, continuing the work of Lagrange.</div></div></div>Servois' 1814 Essay on a New Method of Exposition of the Principles of Differential Calculus, with an English Translation - Introduction
http://www.maa.org/publications/periodicals/convergence/servois-1814-essay-on-a-new-method-of-exposition-of-the-principles-of-differential-calculus-with-an-0
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even">A study and English translation of Servois' attempt to place calculus on a foundation of algebraic analysis without recourse to infinitesimals, continuing the work of Lagrange.</div></div></div>Servois' 1814 Essay on a New Method of Exposition of the Principles of Differential Calculus, with an English Translation
http://www.maa.org/publications/periodicals/convergence/servois-1814-essay-on-a-new-method-of-exposition-of-the-principles-of-differential-calculus-with-an
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even">A study and English translation of Servois' attempt to place calculus on a foundation of algebraic analysis without recourse to infinitesimals, continuing the work of Lagrange.</div></div></div>Servois' 1814 Essay on the Principles of the Differential Calculus, with an English Translation - Acknowledgments and About the Authors
http://www.maa.org/publications/periodicals/convergence/servois-1814-essay-on-the-principles-of-the-differential-calculus-with-an-english-translation-9
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even">The authors provide an analysis and English translation of the argument by a little known French mathematician that calculus should be based on series rather than on infinitesimals.</div></div></div>Servois' 1814 Essay on the Principles of the Differential Calculus, with an English Translation - References
http://www.maa.org/publications/periodicals/convergence/servois-1814-essay-on-the-principles-of-the-differential-calculus-with-an-english-translation-8
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even">The authors provide an analysis and English translation of the argument by a little known French mathematician that calculus should be based on series rather than on infinitesimals.</div></div></div>Servois' 1814 Essay on the Principles of the Differential Calculus, with an English Translation - Conclusions, Recommendations, and Translation
http://www.maa.org/publications/periodicals/convergence/servois-1814-essay-on-the-principles-of-the-differential-calculus-with-an-english-translation-7
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even">The authors provide an analysis and English translation of the argument by a little known French mathematician that calculus should be based on series rather than on infinitesimals.</div></div></div>Servois' 1814 Essay on the Principles of the Differential Calculus, with an English Translation - Criticism of Wronski in the “Reflections”
http://www.maa.org/publications/periodicals/convergence/servois-1814-essay-on-the-principles-of-the-differential-calculus-with-an-english-translation-6
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even">The authors provide an analysis and English translation of the argument by a little known French mathematician that calculus should be based on series rather than on infinitesimals.</div></div></div>Servois' 1814 Essay on a New Method of Exposition of the Principles of Differential Calculus, with an English Translation - A Reader's Guide to Servois' 'Essay'
http://www.maa.org/publications/periodicals/convergence/servois-1814-essay-on-a-new-method-of-exposition-of-the-principles-of-differential-calculus-with-an-6
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even">A study and English translation of Servois' attempt to place calculus on a foundation of algebraic analysis without recourse to infinitesimals, continuing the work of Lagrange.</div></div></div>Servois' 1814 Essay on a New Method of Exposition of the Principles of Differential Calculus, with an English Translation - Functions and Operators
http://www.maa.org/publications/periodicals/convergence/servois-1814-essay-on-a-new-method-of-exposition-of-the-principles-of-differential-calculus-with-an-7
<div class="field field-name-body field-type-text-with-summary field-label-hidden"><div class="field-items"><div class="field-item even">A study and English translation of Servois' attempt to place calculus on a foundation of algebraic analysis without recourse to infinitesimals, continuing the work of Lagrange.</div></div></div>