Editing Exponentiation (section)

===Large exponents===
The [[limit of a sequence]] of powers of a number greater than one diverges; in other words, the sequence grows without bound:
: {{math|''b''<sup>''n''</sup> → ∞}} as {{math|''n'' → ∞}} when {{math|''b'' > 1}}

This can be read as "''b'' to the power of ''n'' tends to [[extended real number line|+∞]] as ''n'' tends to infinity when ''b'' is greater than one".

Powers of a number with [[absolute value]] less than one tend to zero:
: {{math|''b''<sup>''n''</sup> → 0}} as {{math|''n'' → ∞}} when {{math|{{abs|''b''}} < 1}}

Any power of one is always one:
: {{math|1=''b''<sup>''n''</sup> = 1}} for all {{math|''n''}} for {{math|1=''b'' = 1}}

Powers of a negative number <math>b\leq -1</math> alternate between positive and negative as {{math|''n''}} alternates between even and odd, and thus do not tend to any limit as {{math|''n''}} grows.

If the exponentiated number varies while tending to {{math|1}} as the exponent tends to infinity, then the limit is not necessarily one of those above. A particularly important case is
: {{math|(1 + 1/''n'')<sup>''n''</sup> → ''e''}} as {{math|''n'' → ∞}}

See ''{{slink||Exponential function}}'' below.

Other limits, in particular those of expressions that take on an [[indeterminate form]], are described in ''{{slink||Limits of powers}}'' below.