The binomial approximation is the first-order approximation
for . It follows by truncating the binomial series
after its linear term. More precisely, for fixed ,
as . Here is big-O notation indicating a remainder whose magnitude is bounded by a constant multiple of for all sufficiently small . The approximation is exact when or 1.
More things to try:
Weisstein, Eric W. "Binomial Approximation." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/BinomialApproximation.html
.
It follows by truncating the binomial series
,
.
Here 
is big-O notation indicating a remainder whose
magnitude is bounded by a constant multiple of 
for all sufficiently small 
. The approximation is exact when 
or 1.
