An infinite series for the natural logarithm that converges throughout   its domain and makes concavity transparent
  The natural logarithm can be represented by an infinite series that converges for all positive real values of the variable, and which makes concavity patently obvious. Concavity of the natural logarithm is known to imply, among other things, the fundamental inequality between the arithmetic and geometric mean. 
David M. Bradley (University of Maine)
math.CA