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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.

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    $\begingroup$ 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. $\endgroup$ – Dr. Lutz Lehmann Jun 12 at 11:03
  • $\begingroup$ Thank you @LutzL $\endgroup$ – Dunkel Jun 12 at 18:09

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