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Vă rog frumos frumos frumos frumos

Vă Rog Frumos Frumos Frumos Frumos class=

Răspuns :

[tex]a = \dfrac{1}{2}+\dfrac{1}{3}+...+\dfrac{1}{2012} \\ \\ b = \dfrac{1}{2}+\dfrac{2}{3}+\dfrac{3}{4}+...+\dfrac{2011}{2012} \\ \\ a+b = \dfrac{2}{2}+\dfrac{3}{3}+\dfrac{4}{4}+...+\dfrac{2012}{2012} = 1+1+1+...+1 = 1\cdot 2011 = 2011 \\ \\ \dfrac{a+b}{2} = \dfrac{2011}{2} =1005,5[/tex]

[tex]N = \frac{17}{24} + \frac{1717}{2424}^{(101} + \frac{171717}{242424} ^{(10101} + \frac{17171717}{24242424}^{(1010101} \\ \\ N = \frac{17}{24} + \frac{17}{24} + \frac{17}{24} + \frac{17}{24} \\ \\ N = \frac{17 + 17 + 17 + 17}{24} \\ \\ N = \frac{4 \times 17}{24} \\ \\ N = { \frac{68}{24} }^{(4} \\ \\ N = \frac{17}{6} \\ \\ N = 2 \frac{5}{6} [/tex]