The sum of the last ten coefficients in the expansion of $(1+x)^{19}$ when expanded in ascending pow

Question

The sum of the last ten coefficients in the expansion of $(1+x)^{19}$ when expanded in ascending powers of $x$, is

Professor PC Thomas Classes · Answer

By symmetry $\binom{19}{0} + \dots + \binom{19}{9} = \binom{19}{10} + \dots + \binom{19}{19}$. Total sum is $2^{19}$, so half sum is $2^{18}$.