The ratio of the coefficient of the middle term in the expansion of (1+x)20 and the sum of the coefficients of two middle terms in expansion of (1+x)19 is .......
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Official solution
Middle term coefficient of (1+x)20: 20C10.
Middle-term coefficients of (1+x)19: 19C9 and 19C10, whose sum =20C10 (Pascal's identity).
\[\frac{{}^{20}C_{10}}{{}^{19}C_9+{}^{19}C_{10}}=\frac{{}^{20}C_{10}}{{}^{20}C_{10}}=1\]