a, $150 - (100 - 99) + (98 - 97) +...+ (2 - 1)$
$=150 - 1 × 50$
$=100$
b, $\frac{\frac{2}{3} + \frac{2}{5}- \frac{2}{7}}{\frac{8}{3} + \frac{8}{5}- \frac{8}{7}}$
=$\frac{\frac{1}{3} + \frac{1}{5}- \frac{1}{7}}{\frac{4}{3} + \frac{4}{5}- \frac{4}{7}}$
=$\frac{1}{4}$
c,Đặt $A = 1$ + $3^{2}$ + $3^{3}$ + ... + $3^{200}$
⇔$3A = $$3^{3}$ + $3^{4}$ + ... + $3^{201}$
⇔$2A =$$3^{201}$ $- 1$
d, $\frac{\frac{2013}{2} + \frac{2013}{3} +...+ \frac{2013}{2014}}{\frac{2013}{1} + \frac{2012}{2} +...+ \frac{1}{2013}}$
= $\frac{2013.(\frac{1}{2}+\frac{1}{3} +...+\frac{1}{2014})}{(1 + \frac{2012}{2}) + (1 + \frac{2012}{2})+...+ (1 + \frac{1}{2013}) + 1}$
= $\frac{2013.(\frac{1}{2}+\frac{1}{3} +...+\frac{1}{2014})}{2014.(\frac{1}{2}+\frac{1}{3} +...+\frac{1}{2014})}$ = $\frac{2013}{2014}$
