\(\dfrac{2010}{2}\) + \(\dfrac{2010}{6}\) + \(\dfrac{2010}{12}\) + ... + \(\dfrac{2010}{9900}\)

= 2010 . \(\left(\dfrac{1}{1.2}+\dfrac{1}{2.3}+\dfrac{1}{3.4}+...+\dfrac{1}{99.100}\right)\)

= 2010 . \(\left(1-\dfrac{1}{100}\right)\) 

= 1989,9

2010220102 + 2010620106 + 201012201012 + ... + 2010990020109900

= 2010 . (11.2+12.3+13.4+...+199.100)(11.2+12.3+13.4+...+199.100)

= 2010 . (1−1100)(1−1100) 

= 1989,9