a) $2 + 2^2 + 2^3 +\dots + 2^{60}$
$= (2 + 2^2) + (2^3 + 2^4)+\dots +(2^{59} + 2^{60})$
$= 2(1 +2) + 2^3(1 +2) +\dots +2^{59}(1+2)$
$= (1+2)(2+2^3 +\dots + 2^{59})$
$= 3(2+2^3 +\dots + 2^{59})\quad \vdots\quad 3$
b) Ta có:
$3^{450}=3^{150.3}=(3^3)^{150}=27^{150}$
$5^{300}=5^{150.2}=(5^2)^{150}=25^{150}$
Do $27 > 25$
nên $27^{150} > 25^{150}$
hay $3^{450}>5^{300}$