#### Answer

a. 67108863
b. 134217726

#### Work Step by Step

We know that,
$1 + r + r^2 + ··· + r^n = \frac{r^{n+1}− 1}{r − 1}$
a)
Thus,
$1 + 2 + 2^2 + ··· + 2^{25}$
= $\frac{2^{25+1} − 1}{2-1}$
= $\frac{2^{26} − 1}{2-1}$
= $2^{26} − 1 = 67108863$
b.
$2 + 2^2 + 2^3 + ··· + 2^{26}$
= $2\times(1 + 2 + 2^2 + ··· + 2^{25} )$
= $2\times(67108863)$ [ by (a) ]
= 134217726