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Fie numerele [tex]a=1+\frac{1}{3}+\frac{1}{5}+\ldots+\frac{1}{2009}[/tex] și [tex]b=\frac{1}{2}+\frac{1}{4}+\frac{1}{6}+\ldots+\frac{1}{2010}[/tex].
Arătați că [tex]a-b=\frac{1}{1006}+\frac{1}{1007}+\ldots+\frac{1}{2010}[/tex].
Sagot :
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