Question

[Đào Hương Nguyên]

hãy so sánh
5^{^}37-1/5^38-1 và 5^36+1/5^37+1
cứu m vs các bạn oiiiiiiiii

Answer 1

[Nguyễn Lê Phước Thịnh]

\(5\cdot\dfrac{5^{37}-1}{5^{38}-1}=\dfrac{5^{38}-5}{5^{38}-1}=1-\dfrac{4}{5^{38}-1}\)

\(\dfrac{5\left(5^{36}+1\right)}{5^{37}+1}=\dfrac{5^{37}+5}{5^{37}+1}=1+\dfrac{4}{5^{37}+1}\)

mà \(-\dfrac{4}{5^{38}-1}< \dfrac{4}{5^{37}+1}\)

nên \(5\cdot\dfrac{5^{37}-1}{5^{38}-1}< 5\cdot\dfrac{5^{36}+1}{5^{37}+1}\)

=>\(\dfrac{5^{37}-1}{5^{38}-1}< \dfrac{5^{36}+1}{5^{37}+1}\)