Giải thích các bước giải:
Ta có:
$A=1+5+5^2+5^3+...+5^{98}$
$\to 5A=5+5^2+5^3+5^4+...+5^{99}$
$\to 5A-A=5^{99}-1$
$\to 4A=5^{99}-1$
$\to A=\dfrac{5^{99}-1}{4}$
Mặt khác :
$A=1+5+5^2+5^3+...+5^{98}$
$\to A=(1+5+5^2)+(5^3+5^4+5^5)+...+(5^{96}+5^{97}+5^{98})$
$\to A=(1+5+5^2)+5^3(1+5+5^2)+...+5^{96}(1+5+5^2)$
$\to A=(1+5+5^2)(1+5^3+...+5^{96})$
$\to A=31(1+5^3+...+5^{96})$
$\to A\quad\vdots\quad 31$
$\to\dfrac{5^{99}-1}{4}\quad\vdots\quad 31$
$\to đpcm$
