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September 2009
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geometric series

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Those who understand compound interest are destined to collect it. Those who don't are doomed to pay it - or so says a well-known source of financial advice. But what is compound interest, and why is it so important? John H. Webb explains.

Tags: compound interest : present value : future value : rule of 70 : logarithm : Maclaurin series : geometric series


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The harmonic series is far less widely known than the arithmetic and geometric series. However, it is linked to a good deal of fascinating mathematics, some challenging Olympiad problems, several surprising applications, and even a famous unsolved problem. John Webb applies some divergent thinking, taking in the weather, traffic flow and card shuffling along the way.

Tags: logarithm : geometric series : convergence : arithmetic series : harmonic series : divergence


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Tags: geometric series : convergence : limit : Zeno's paradoxes : Achilles Paradox : Arrow Paradox : worldline : relativity


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Infinite series occupy a central and important place in mathematics. C. J. Sangwin shows us how eighteenth-century mathematician Leonhard Euler solved one of the foremost infinite series problems of his day.

Tags: geometric series : convergence : harmonic series : divergence : infinite series : integral test : Euler's solution to the Basel problem : sine : power series