Perhaps someone should forward this upstream.
$\sum_{ n > 0} \pi^n$ certainly diverges though
mpmath claims it equals -pi/(pi-1)
sage: import mpmath
sage: mpmath.mp.pretty=True;mpmath.mp.dps=40
sage: r1=mpmath.nsum(lambda n: mpmath.pi**n,[ 1, mpmath.inf])
sage: r1
-1.466942206924259859983394813233667573143
sage:
sage: r2=-mpmath.pi/(mpmath.pi - 1)
sage: r1-r2
0.0
sage: r3=mpmath.nsum(lambda n: mpmath.mpf('2')**n,[ 1, mpmath.inf]);r3
-2.0
Computing zeta(2) appears OK:
sage: z2=mpmath.nsum(lambda n: 1/n**2,[ 1, mpmath.inf]);z2
1.644934066848226436472415166646025189219
sage: z2 - mpmath.zeta(2)
0.0
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