Question

$\frac{1 + 2 + 2 {}^{2} + ... + 2 {}^{60} }{2 {}^{61} - 1}$

Answer 1

$\frac{1+2+2^2+... +2^{60}}{2^{61}-1} = \frac{1+2+2^2+... +2^{60}}{(2-1)(1+2+2^2+... +2^{60})} = \frac{1}{2-1} = 1$