Докажите что 1/2<1/1001+1/1002+...+1/2000<1

Question

Докажите что 1/2<1/1001+1/1002+...+1/2000<1</p>

Answer 1

\frac{1}{2000}+\frac{1}{2000}+...+\frac{1}{2000}=1000*\frac{1}{2000}=\frac{1}{2};" alt="\frac{1}{1001}+\frac{1}{1002}+...+\frac{1}{2000}>\frac{1}{2000}+\frac{1}{2000}+...+\frac{1}{2000}=1000*\frac{1}{2000}=\frac{1}{2};" align="absmiddle" class="latex-formula">

 

Answer 2

1-(1/2)+(1/3)-(1/4)+...+(1/1999)-(1/2000) =
= (1/1001)+(1/1002)+...+(1/2000).