The following code was run using sympy version 1.0, python version 3.4,
Anaconda installation.
import sympy as spy
import sympy.abc as abc
N, k = spy.symbols('N, k', positive = True)
es = 1 - (1 - 1/(2*N))**k
e = 2*N*es
spy.pprint(e)
c0 = spy.limit(e, N, spy.oo)
spy.pprint(c0)
c1 = spy.limit(N*(e-c0), N, spy.oo)
spy.pprint(c1)
c2 = spy.limit((e-c0-c1/N)*(N*N), N, spy.oo)
spy.pprint(c2)
c2x = spy.limit(e*N*N-c0*N*N-c1*N, N, spy.oo)
spy.pprint(c2x)
It prints
⎛ k ⎞
⎜ ⎛ 1 ⎞ ⎟
2⋅N⋅⎜- ⎜1 - ───⎟ + 1⎟
⎝ ⎝ 2⋅N⎠ ⎠
k
2
k k
- ── + ─
4 4
-∞
3 2
k k k
── - ── + ──
24 8 12
As you can see, the result for c2 is wrong, although it is able to
calculate c2x correctly.
Can someone please clarify what is going on?
Thanks!
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