Help with Maple's incorrecty
Nguyen Lam
I could not find my mistake when I use the following computing with Maple.
> restart;
> sum((2*n^2+3*n)/sqrt(5+n^5), n = 1 .. infinity):
> evalf(%);
1.761936848
That is wrong result, since the series is devergent.
Please help me to find out my mistake.
thanks,
Lam
Nasser Abbasi
"Nguyen Lam" <nctu...@yahoo.com> wrote in message
news:25806478.1226856320...@nitrogen.mathforum.org...
You are not doing anything wrong. This is clearly a bug. I tried in Maple 12
also and get the same resullt. Here is Mathematica answer:
In[1]:= s = Sum[(2*n^2 + 3*n)/Sqrt[5 + n^5], {n, 1, Infinity}]
During evaluation of In[1]:= Sum::div:Sum does not converge. >>
Out[1]= Sum[(3*n + 2*n^2)/Sqrt[5 + n^5], {n, 1, Infinity}]
Preben Alsholm
> "Nguyen Lam" <nctu...@yahoo.com> wrote in message
> news:25806478.1226856320...@nitrogen.mathforum.org...
>> Dear friends,
>> I could not find my mistake when I use the following computing with Maple.
>>> restart;
>>> sum((2*n^2+3*n)/sqrt(5+n^5), n = 1 .. infinity):
>>> evalf(%);
>> 1.761936848
>>
>> That is wrong result, since the series is devergent.
>> Please help me to find out my mistake.
>> thanks,
>> Lam
>
> You are not doing anything wrong. This is clearly a bug. I tried in Maple 12
> also and get the same resullt.
This is most likely not a bug, since we in the help page for Numerical
Summation (?evalf,Sum) can find the comment,
"In the case of infinite sums, Levin's u-transform is used, which has
the additional effect that sums that formally diverge may return a
result that can be interpreted as evaluation of the analytic extension
of the series for the sum (see the examples below)."
The help page gives the example
evalf(Sum(1/sqrt(x), x=1..infinity));
which returns the negative result -1.460354509.
Preben Alsholm
ma...@rogers.com
The help-page ?evalf/Sum also describes its behaviour under the
environment variable _EnvFormal.
> S := Sum((2*n^2+3*n)/sqrt(5+n^5), n = 1 .. infinity):
> evalf(S);
1.761936848
> forget(evalf);
> _EnvFormal:=false:
> evalf(S);
Float(infinity)