Question

Bài 1: So sánh

\(M=\frac{20^{30}+2}{20^{31}+2}\) và   \(N=\frac{20^{31}+2}{20^{32}+2}\)

Answer 1

Vì N<1

=> N= 20^31+2/20^32+2

<20^31+2+38/ 20^32+2+38

=20^31+40/ 20^32+40

=20.(20^30+2) / 20.(20^31+2)

=20^30+2 / 20^32+2 = M

Vậy N<M

Answer 2

\(N=\frac{20^{31}+2}{20^{32}+2}=\frac{20^{31}+2+18}{20^{32}+2+18}=\frac{20^{31}+20}{20^{32}+20}=\frac{10.\left(20^{30}+2\right)}{10.\left(20^{31}+2\right)}\)\(=M\)

\(\Rightarrow M=N\)