Question

So Sánh 

a) 8^18 + 1/8^19 +1 và 8^23 + 1/8^24 +1

 

Answer 1

Áp dụng tính chất \(\frac{a}{b}< 1\Rightarrow\frac{a}{b}< \frac{a+m}{b+m}\left(m\in N\right)\)

Ta có: \(\frac{8^{23}+1}{8^{24}+1}< \frac{8^{23}+1-1+8^5}{8^{24}+1-1+8^5}=\frac{8^{23}+8^5}{8^{24}+8^5}=\frac{8^5.\left(8^{18}+1\right)}{8^5.\left(8^{19}+1\right)}=\frac{8^{18}+1}{8^{19}+1}\)

Vậy \(\frac{8^{23}+1}{8^{24}+1}< \frac{8^{18}+1}{8^{19}+1}\)

Answer 2

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