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The coefficient of middle term in the expansion of $$(1 + x)^{40}$$ is
$$\frac{1.3.5 ... 39}{20!}2^{20}$$
$$\frac{1.3.5 ... 39}{20!}$$
$$\frac{21.22 ... 40}{20!}$$
$$40!2^{20}$$
The middle term will be the 21st term whose coefficient will be $$^{^{40}C}20=\frac{40!}{20!20!}=\frac{21\times\ 22\times\ 23.....\times\ 40}{20!}$$
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