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Student Support Forum: 'Converging Summations' topicStudent Support Forum > General > Archives > "Converging Summations"

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Mike Willhide
03/08/99 06:24am

Hi. Newbie here. I'm working on a mechanics problem that requires me to find the
limit of a sum as the iterator goes to infinity. Let's see if I can type
this...

Summation from n=0 to n=infinity of:

{ e^(2n) * h } + { e^(2n+1) * h}

This limit exists if e < 1. Otherwise, it diverges. Here is the meat of my
question:

How do I tell Mathematica that e will always be less than 1 such that it
produces the limit as a function of e and h (analytical solution)?

I can obtain numerical solutions by using:

Limit[ theSummationPresentedAbove /. {e->NumberLessThanOne, h->AnyValue},
n->infinity ]

Does an analytical solution exist, or will it be different with each value of e
and h?

Also, this doesn't work, can you tell me why?

f[MyH_,MyE_] := Limit[ Sum[ {MyE^(2n) * MyH + MyE^(2n+1) * MyH} ], {n, 0,
infinity}]

It just returns f[ a, b].

Sorry about the length of this post, but it's hard to get these things across
without the luxury of Mathematica's notation. Thanks a bundl

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