Question

[chipchip]

Cho A=1/2^2+1/3^2+1/4^2+.......+1/20^2 .Chung to rang A<1

Cho A=1/2^2+1/3^2+1/4^2+........+1/20^2 .Chung minh A<1

Chu thich / La phan so 

^ la mu 

Answer 1

[Arima Kousei]

\(Ta\)có : 

\(\frac{1}{2^2}< \frac{1}{1.2};\frac{1}{3^2}< \frac{1}{2.3};...;\frac{1}{20^2}< \frac{1}{19.20}\)

\(\Rightarrow\frac{1}{2^2}+\frac{1}{3^2}+...+\frac{1}{20^2}< \frac{1}{1.2}+\frac{1}{2.3}+...+\frac{1}{19.20}\)

\(\Rightarrow A< 1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{19}-\frac{1}{20}\)

\(\Rightarrow A< 1-\frac{1}{20}< 1\left(Đpcm\right)\)

Chúc bạn học tốt !!!