tfv tfv - 2 months ago 6
Python Question

Why does SymPy not work properly with real numbers?

I am trying to evaluate an infinite sum in SymPy. While the first expression is calculated the way I expect it, SymPy seems to have trouble with the second expression.

from sympy import *
n = symbols('n')
print Sum((2)**(-n), (n, 1, oo)).doit()
print Sum((0.5)**(n), (n, 1, oo)).doit()


Results in:

1
Sum(0.5**n, (n, 1, oo))


I assume that the reason is that I am using a float number instead of an integer value.

Is there a way to approximate the sum instead?

Answer

From the docs:

If it cannot compute the sum, it returns an unevaluated Sum object.

Another way to do this would be:

In [40]: Sum((Rational(1,2))**(n), (n, 1, oo)).doit()
Out[40]: 1

Yet another way to do this:

In [43]: Sum((0.5)**(n), (n, 1, float('inf'))).doit()
Out[43]: 1.00000000000000

To approximate, you can take a sufficiently large number instead of infinity:

In [51]: import sys

In [52]: Sum((0.5)**(n), (n, 1, sys.maxint)).doit()
Out[52]: 1.00000000000000
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