Sigma NotationDate: 4/14/96 at 3:16:17 From: tnicpwr Subject: sigma notation Dear Dr Math, I am trying to find questions regarding sigma notation. For example: (with the sigma notation sign in front)5+6r, (with the sigma notation sign in front)r(r+1). Thank you. Date: 4/14/96 at 14:47:47 From: Doctor Syd Subject: Re: sigma notation Hello! I'm not quite sure what you are looking for... you want questions regarding sigma notation? Are you curious about infinite series and the convergence/divergence of series? I'm not sure in what direction your question is going. But, since you asked for questions regarding sigma notation, I'll give you one: For this question let {E n=0 to n=infinity} denote the sigma with values of n going from 0 to infinity. Calculate: E n=0 to n= infinity ( ar^n), where a and r are constants. This is an example of an infinite series. You'll find that depending on the value of r, sometimes it converges (this means the sum is a finite number), and sometimes not. I don't know if you've worked with infinite series before, or only finite series, but infinite serious have fascinated mathematicians for a long time. Another famous infinite serious is called the harmonic series: E n=1 to n= infinity 1/n This series actually diverges (the sum goes to infinity) even though the terms in the end of the sum get really small. Pretty neat, eh? See if you can prove why. It involves a trick of sorts, but try to think about it! I hope this helps. If I didn't answer your question, write back and re-ask it in different terms. -Doctor Syd, The Math Forum |
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