Bạn tham khảo :
$(1)$
$A = 5+5^2+5^3+...+5^{100}$
$5A = 5^2 + 5^3 + 5^4 + ... + 5^{101}$
$5A - A = ( 5^2 + 5^3 + 5^4 + ... + 5^{101}) - ( 5+5^2+5^3+...+5^{100})$
$4A = 5^{101} - 5$
$A = \dfrac{5^{101} - 5}{4}$
$(2)$
$A = 5+5^2+5^3+...+5^{100}$
$= (5+5^2) + (5^3 +5^4) + ... + (5^{99} + 5^{100}$
$= 5(1+5) + 5^3(1+5) +... + 5^{99}(1+5)$
$= 5.6 + 5^3.6 + ... + 5^{99}.6 $
$= 30 . 1 + 5^2 . 5.6 +... + 5^{98} .5 .6$
$= 30 . 1 + 5^2 . 30 + ... 5^{98} .30$
$= 30 (1+5^2 + ... + 5^{98}) \vdots 30$
