Re: Evaluate

[James Sherman Jr.]

On Sat, Feb 9, 2013 at 1:49 PM, Sifiso <address@hidden> wrote:
> Please help me evaluate the following series sum(u(n)) from n=1 to inifinity, 
> in which u(n) is not known explicitly but given in terms of a recurrence 
> relation. You should stop the summation when the absolute value of 
> u(n)<10^-8. u(n+1)=(u(n))^2 with u(1)=0.5
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I'm a bit confused about the question.  The summation from 1 to
infinity of a geometric series of infinite length (see
http://en.wikipedia.org/wiki/Geometric_series if you're unfamiliar
with geometric series).

If you don't want to go to infinity, but stop when u(n)<10^-8, then
you need to find out when that n is, so you're gonna need to find out
u(n) explicitly anyway.  Your question seems to indicate that it can't
be, but it is easy enough, just u(n) = (0.5)^n  .  Thus, solve when
(0.5)^n = 10^-8 and use the formula for a geometric series of length
n.

Hope this helps,

James Sherman