Tag Archive for: infinite series

geometric series

Series in Mathematics: From Zeno to Quantum Theory

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Introduction Series play a decisive role in many branches of mathematics. They accompanied mathematical developments from Zeno of Elea (##5##-th century…
Odd Sums

Explore the Fascinating Sums of Odd Powers of 1/n

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The goal is to get a little bit closer to the values of the zeta function (ζ(s)) and the eta function (η(s)) for some odd values of s. This insight is…
fourierseries2

Learn Further Sums Found Through Fourier Series

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In an earlier insight, I looked at the Fourier series for some simple polynomials and what we could deduce from those series. There is a lot more to be…
FourierSeries

Using the Fourier Series To Find Some Interesting Sums

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Preliminaries If f(x) is periodic with period 2p and f’(x) exists and is finite for -π<x<π, then f can be written as a Fourier series: [itex]f(x)=\sum_{n=-\infty}^{\infty}a_{n}e^{inx}…
999

Is 1 Equal to 0.999…? Rigorous Proof Explained

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Yes, 1 equals 0.999... exactly, not approximately. This is a proven mathematical fact once the notation 0.999... and the concept of an infinite sum are…