Bài 5 :
$O = 1+3^1+3^2+3^3+....+^{100}$
$⇒3.O = 3+3^2+3^3+3^4+....+3^{101}$
$⇒3.O-O = (3+3^2+3^3+3^4+....+3^{101})-(1+3^1+3^2+3^3+....+^{100})$
$⇒2.O = 3^{101}-1$
$⇒O = \dfrac{3^{101}-1}{2}$
Vậy $O = \dfrac{3^{101}-1}{2}$
Bài 6 :
$E =1.2+2.3+3.4+....+1001.1002$
$⇒3E = 1.2.3+2.3.(4-1)+3.4.(5-2)+....+1001.1002.(1003-1000)$
$=1.2.3-1.2.3+2.3.4-2.3.4+3.4.5-....-1000.1001.1002+1001.1002.1003$
$=1001.1002.1003$
$⇒E = 1001.334.1003$