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# Using the Binomial theorem indicate which number is larger $(1-1)^{10000}$ or 1000

Toolbox:
• $(1+x)^n=nC_0+nC_1x+nC_2x^2+.....+nC_1x^r+.....+nC_xx^n$
$(1.1)^{10000}=[1+(.1)]^{10000}$
Expanding by binomial theorem
$C(10000,0)(1)^{10000}+C(10000,1)(1)^{10000-1}(.1)$
$1+1000\times .1$+other terms
$1000$+other terms of the expansion.
Hence $(1.1)^{10000} > 1000$