On 16/07/2009, at 2:30 PM, Roslina Zakaria wrote:
> Hi R-users,
>
> Could anybody show me how to write a code to evaluate sum(z[i] + sum
> (k[j]*(z[i])^(k[j])), i=1 to 4, j=0 to infinity) ?
No. No-one can. It is conceptually impossible.
(a) Computers cannot do infinite sums; they can only do finite ones.
(b) Attempting to approximate infinite sums by finite ones that
computers
can do is theoretically possible, but fraught with peril. E.g. try
summing
{1/(j+1)} from 0 to infinity that way. You may, after a long while,
get a
finite answer .....
(c) What is k[j] equal to? You must have an expression for it, elsewise
your question makes no sense at all.
If the sequence k[j] is sufficiently nice then you may be able to
determine
error bounds. I.e. for a given epsilon, find an M_0 such that the
sum from
0 to M is within epsilon of the sum to infinity for any M >= M_0.
The sum from 0 to M is easy to calculate.
cheers,
Rolf
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