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 _____________.

Coeff. of middle term in (1 + x)^(20) = ^20C_10 \ Sum of coeff. of two middle terms in (1 + x)^(19) = ^19C_9 + ^19C_10 So required ratio = ^20C_10 / ^19C_9 + ^19C_10 = ^20C_10 / ^20C_10 = 1

The ratio of the coefficient of the middle term in the ... | null (Mathematics)

Coeff. of middle term in (1 + x)²⁰ =

{}^{20}{C_{10}} \\\\

& Sum of coeff. of two middle terms in (1 + x)¹⁹ =

{}^{19}{C_{9}} + {}^{19}{C_{10}} \\\\

So required ratio =

{{{}^{20}{C_{10}}} \over {^{19}{C_9}{ + ^{19}}{C_{10}}}} = {{^{20}{C_{10}}} \over {^{20}{C_{10}}}} = 1

Explanation

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