Sum of the last $20$ coefficients in the expansion of ${(1 + x)}^{39}$, when expanded in ascending power of $x$ is

There are $40$ terms in the expansion of ${\left(1+x\right)}^{39}.$ Sum of the last $20$ coefficients is
    $S{=}^{39}{C}_{20}{+}^{39}{C}_{21}+\dots {+}^{39}{C}_{38}{+}^{39}{C}_{39}$
$\Rightarrow S{=}^{39}{C}_{19}{+}^{39}{C}_{18}+\dots {+}^{39}{C}_1{+}^{39}{C}_0$

                                                     [Using ${ }^n{C}_r{=}^n{C}_{n-r}$]
Adding the above two expressions, we get
 $\begin{array}{l} 2S{=}^{39}{C}_0{+}^{39}{C}_1+\dots {+}^{39}{C}_{39}=2^{39}\\ \Rightarrow S=2^{38}\end{array}$