Question

Chứng minh rằng:

S= 1/2^2 + 1/3^2 + 1/4^2 +.....+ 1/200^2<1

Answer 1

Ta có:

 

S<\(\frac{1}{1.2}+\frac{1}{2.3}+\frac{1}{3.4}+...+\frac{1}{199.200}\)

S<\(\frac{1}{1}-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+...+\frac{1}{199}-\frac{1}{200}\)

S<1-\(\frac{1}{200}=\frac{199}{200}