Let n be a positive integer. Let A =Σ_k =0^n (-1)^k n_C_k [(1/2)^k +(3/4)^k +(7/8)^k +(15/16)^k +(31/32)^k ] If 63 A =1-1/(2^30), then n is equal to…

Let n be a positive integer. Let $\displaystyle \mathrm{A}=\sum_{\mathrm{k}=0}^{\mathrm{n}}(-1)^{\mathrm{k}} \mathrm{n}_{\mathrm{C}_{\mathrm{k}}}\left[\left(\frac{1}{2}\right)^{\mathrm{k}}+\left(\frac{3}{4}\right)^{\mathrm{k}}+\left(\frac{7}{8}\right)^{\mathrm{k}}+\left(\frac{15}{16}\right)^{\mathrm{k}}+\left(\frac{31}{32}\right)^{\mathrm{k}}\right]$ If $\displaystyle 63 \mathrm{~A}=1-\frac{1}{2^{30}}$, then n is equal to \_\_\_\_.