linguistic:paraphrasing, structural:expansion, information:classification
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.