Question

a. So sánh phân số: 15/301 với 25/499

b. So sánh tổng S = 1/2 + 1/2² + 1/3² + ... + n/2ⁿ +...+ 2007/2²⁰⁰⁷  với 2 (n € N*)

Answer 1

a) Ta có:
\(\frac{15}{301}>\frac{15}{300}=\frac{1}{20}\)

\(\frac{25}{499}< \frac{25}{500}=\frac{1}{20}\)

Vì \(\frac{1}{20}=\frac{1}{20}\) nên \(\frac{15}{301}>\frac{1}{20}>\frac{25}{499}\) hay \(\frac{15}{301}=\frac{25}{499}\)

Vậy \(\frac{15}{301}>\frac{25}{499}\)

Answer 2

a)Ta có:\(\frac{15}{301}\)<\(\frac{15}{300}\)=\(\frac{1}{20}\)=\(\frac{25}{500}\)<\(\frac{25}{499}\)

Vì \(\frac{15}{301}\)<\(\frac{25}{500}\)<\(\frac{25}{499}\)

\(\Rightarrow\)\(\frac{15}{301}< \frac{25}{499}\)(đpcm)

Answer 3

Còn câu b  thì sao.