1/210 + 2/201 + .. + 201/201 =
= (1 + 2 + .. + 201)/201
= 201×202:2/201
= 201×101/201
= 101
[tex]\dfrac{1}{201}+\dfrac{2}{201}+...+\dfrac{201}{201} = \\ \\ = (1+2+...+201)\cdot \dfrac{1}{201} = \\ \\ = \dfrac{201\cdot (201+1)}{2}\cdot \dfrac{1}{201} = \\ \\ =\dfrac{201+1}{2} = \\ \\ =\dfrac{202}{2} = \\ \\ = \boxed{101}[/tex]