integral test
http://plus.maths.org/content/taxonomy/term/506
enAn infinite series of surprises
http://plus.maths.org/content/infinite-series-surprises
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C. J. Sangwin </div>
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<img class="imagefield imagefield-field_abs_img" width="130" height="130" alt="" src="http://plus.maths.org/content/sites/plus.maths.org/files/issue19/features/infseries/icon.jpg?1007164800" /> </div>
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Infinite series occupy a central and important place in mathematics. <b>C. J. Sangwin</b> shows us how eighteenth-century mathematician Leonhard Euler solved one of the foremost infinite series problems of his day. </div>
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<div class="pub_date">Mar 2002</div>
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<h3>Introduction</h3>
[maths]An infinite sum of the form \setcounter{equation}{0} \begin{equation} a_1 + a_2 + a_3 + \cdots = \sum_{k=1}^\infty a_k, \end{equation} is known as an infinite series. Such series appear in many areas of modern mathematics. Much of this topic was developed during the seventeenth century. Leonhard Euler continued this study and in the process solved many important problems.<p><a href="http://plus.maths.org/content/infinite-series-surprises" target="_blank">read more</a></p>http://plus.maths.org/content/infinite-series-surprises#comments19convergencedivergenceEuler's solution to the Basel problemgeometric seriesharmonic seriesinfinite seriesintegral testpower seriesSat, 01 Dec 2001 00:00:00 +0000plusadmin2202 at http://plus.maths.org/content