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1 pe 100+2 pe 100+...99 pe 100 pls

Răspuns :

Aplicam formula:   [tex]1+2+3+..+n = \frac{n*(n+1)}{2} [/tex].

[tex]\frac{1}{100} + \frac{2}{100} + \frac{3}{100} +...+ \frac{99}{100} = \frac{1}{100} (1+2+3+...+99) = \frac{1}{100} * \frac{99*100}{2} \\ \\ = \frac{99*100}{100*2} = \frac{99}{2} = 49,5[/tex]
[tex]\frac{1}{100}+\frac{2}{100}+\;...\;+\frac{99}{100}=\frac{1+2+...+99}{100}=\frac{99*100}{2}:(100)=99/2=49,5[/tex]