The sum of the last 30coefficients of power sof x  the binomial expansion  of $(1+x{)}^{59}$ is

We have,

$\begin{array}{r}(1+x{)}^{59}=\sum _{r=0}^{59}{ }^{59}{\mathrm{C}}_r{x}^r\\ \Rightarrow 2^{59}=\sum _{r=0}^{59}{ }^{59}{\mathrm{C}}_r\\ \Rightarrow 2^{59}=2\left(\sum _{r=0}^{29}{ }^{59}{\mathrm{C}}_r\right)\\ \Rightarrow 2^{58}=\sum _{r=0}^{29}{ }^{59}{\mathrm{C}}_r\\ \Rightarrow 2^{58}=\sum _{r=0}^{29}{ }^{59}{\mathrm{C}}_{59}\dots \end{array}$

$\Rightarrow \sum _{r=0}^{29}{ }^{59}{C}_{59-r}=2^{58}$