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What exactly does the convergence of an infinite series tell us? What does it mean? The goal of this tutorial is to guide you through the processes used to analyze the convergence of an infinite series, and to uncover its importance in relation to other areas of mathematices.
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www.math.unh.edu/~jjp/radius/radius.html
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Geometric series - Wikipedia, the free encyclopedia
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In mathematics, a geometric series is a series with a constant ratio between successive terms. For example, the series is geometric, because each term except the first can be obtained by multiplying...
en.wikipedia.org/wiki/Geometric_series
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© 1998-2009 by Przemyslaw Bogacki...
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www.math.odu.edu/~bogacki/citat/series/index.html
www.math.odu.edu/~bogacki/citat/series/index.html
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Note: If your WWW browser cannot display special symbols, like 2, then click here for the alternative Infinite Series page. ... Infinite series: An infinite series is the sum of infinitely many numbers, like 1+2+3+4+... Clearly, this sum is infinite; it is said to diverge. This series trivially sums to zero: 0=0+0+0+0+...
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www.jimloy.com/algebra/series.htm
www.jimloy.com/algebra/series.htm
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Infinite series. An infinite series is an expression like this: S = 1 + 1/2 + 1/4 + 1/8 + ... The dots mean that infinitely many terms follow. ...
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www.math.utah.edu/~carlson/teaching/calculus/series.htm...
www.math.utah.edu/~carlson/teaching/calculus/series.html
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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. ... is known as an infinite series. Such series appear in many areas of modern mathematics. Much of this topic...
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plus.maths.org/issue19/features/infseries/index.html
plus.maths.org/issue19/features/infseries/index.html
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In this tutorial, we review some of the most common tests for the convergence of an infinite series $$ \sum_{k=0}^{\infty} a_k = a_0 + a_1 + a_2 + \cdots $$ The proofs or these tests are interesting, so we urge you to look them up in your calculus text.
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www.math.hmc.edu/calculus/tutorials/convergence/
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We say that an infinite series with a sum converges. Some series don't converge, like 1 + 1/2 + 1/3 + 1/4 + ..., the harmonic series.. To see that the partial sums go off to infinity, note that we have 1 and 1/2 and then ;
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www.csm.astate.edu/seqser.html
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+ 1/2 n + ..., which is defined and equal to 2. When the sum of an infinite series is finite and definable, then that series and its corresponding seqeuence converge. Otherwise, the series and its corresponding sequence diverge.
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whatis.techtarget.com/definition/0,,sid9_gci804476,00.h...
whatis.techtarget.com/definition/0,,sid9_gci804476,00.html
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