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Aratati ca √1+√2+...+√2010 mai mic  decat 2010•2011 supra 4

Răspuns :

√1+√2+....+√2010=√2010·√2011/2
Ridicam la patrat si obtinem:
|2010|·|2011|/4
Stim ca:
a·b≤|a|·|b|
Aplicand in relatia noastra obtinem:
2010·2011/4≤|2010|·|2011|/4
Spor la lucru!