section_path: Integer exponents/Large exponents
section_name: Large exponents
paragraph_text: Large exponents
  
  The limit of a sequence of powers of a number greater than one diverges; in other words, the sequence grows without bound:
  
  This can be read as " b to the power of n tends to +∞ as n tends to infinity when b is greater than one".
  
  Powers of a number with absolute value less than one tend to zero:
  
  Any power of one is always one:
  
  Powers of –1 alternate between 1 and –1 as n alternates between even and odd, and thus do not tend to any limit as n grows.
  
  If b < –1, b alternates between larger and larger positive and negative numbers as n alternates between even and odd, and thus does not tend to any limit as n grows.
  
  If the exponentiated number varies while tending to 1 as the exponent tends to infinity, then the limit is not necessarily one of those above. A particularly important case is
  
  See § Exponential function below.
  
  Other limits, in particular those of expressions that take on an indeterminate form, are described in § Limits of powers below.