# Binomial Approximation with Small Exponent

Find an approximation for the expression $$(1 + x)^n$$, where $$0 < x < C$$ and $$n$$ is positive but small.
$$C$$ is arbitrarily large (<< 1000) and $$n$$ is arbitrarily small ($$n << 0.01$$). Is there a known expression for such a case?

Any sugestions are welcomed. Thank you.

• Would $\exp(n\ln(1+x))\approx 1+n\ln(1+x)+O(n^2)$ help? I do not think you can do better than the exponential power series if $n$ is the only small quantity. – Dr. Lutz Lehmann Jun 12 at 11:03
• Thank you @LutzL – Dunkel Jun 12 at 18:09