MATHEMATICSMAGAZINE
302
Remark2. Any family of nonnegative series {Enfp(n): p > 0) for which the convergence or the divergence is known, should, by a similar analysis, lead to another test
for convergence.
Remark 3. From the test above it follows that the Dirichlet series
an > 0 for all n
converges if
e
T
and diverges if
En;->alnS
with
log an
_a
log n~
s <-ilo
s > - h log an
log n
-
Acknowledgement. Thanks to Adam Fieldsteel for pointing out an error in an earlier draft of this note.
REFERENCE
1. Ross, K. A., Elementary Analysis: The Theory of Calculus, Springer-Verlag New York, 1986.
Proofwithout Words:
The Volume of a Hemispherevia Cavalieri'sPrinciple*
V-.,u-.P*rJ
_~~~~~~~
_
t
I~
I
S),21~~~~~
~
~~~~V=VmI22ir
I
,
tC
r.
21rr-Frr3
r-,
.......
2irr
*Tzu Geng, son of the most celebrated mathematician in ancient China, Tzu Chung Chih, was believed
to be the first to develop the principle in the 5th century A.D.
-SIDNEY
H.
KUNG
JACKSONVILLE UNIVERSITY
JACKSONVILLE,
FL 32211
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