Question

[mai phuong]

so sánh :    H=119^209 +1/119^210 +1           và            K=119^210 +1 /119^211 +1

Answer 1

[Nguyễn Tuấn Minh]

\(119H=\frac{119\left(119^{209}+1\right)}{119^{210}+1}=\frac{119^{210}+119}{119^{210}+1}=1+\frac{118}{119^{210}}\)

\(119K=\frac{119\left(119^{210}+1\right)}{119^{211}+1}=\frac{119^{211}+119}{119^{211}+1}=1+\frac{118}{119^{211}+1}\)

Vì 119²¹¹+1>119²¹⁰+1 nên \(\frac{118}{119^{211}+1}< \frac{118}{119^{210}+1}\)

\(=>119K< 119H\)

\(=>K< H\)