Đáp án:Giải thích các bước giải:
a) $A=5^{50}-$ $5^{48}+$ $5^{46}-$ $5^{44}+...$ $5^{6}-$ $5^{4}+$ $5^{2}-1$
$⇒ 25A=5^{52}-$ $5^{50}+$ $5^{48}-$ $5^{46}+...$ $5^{8}-$ $5^{6}+$ $5^{4}-$ $5^{2}$
$\text{⇒ A + 25A = }$ $5^{52}-1$
$\text{⇒ 26A = }$ $5^{52}-1$
$⇒ A=\dfrac{5^{52}-1}{26}$
b) ta có : $\text{ 26A = }$ $5^{52}-1$
$\text{⇒ 26A + 1 = }$ $5^{52}=$$5^{n}$
$\text{⇒ n = 52 }$
c) $A=5^{50}-$ $5^{48}+$ $5^{46}-$ $5^{44}+...$ $5^{6}-$ $5^{4}+$ $5^{2}-1$
$A=(5^{50}-$ $5^{48})+($ $5^{46}-$ $5^{44})+...$ $(5^{6}-$ $5^{4})+($ $5^{2}-1)$
$A=5^{48}.($ $5^{2}-1)+$ $5^{44}($ $5^{2}-1)+...+$ $5^{4}($ $5^{2}-1)+24$
$A=5^{48}.24+$ $5^{44}.24+...$ $5^{2}.24+24$
$A=5^{2}.4($ $5^{46}.6+$ $5^{42}.6+...+6)+24$
$A=100^{}($ $5^{46}.6+$ $5^{42}.6+...+6)+24$ $\text{chia 100 dư 24 . }$
