Răspuns :

Răspuns:

Explicație pas cu pas:

a = 1/5 +7/10-1/2 + 8/15-1/3 +

  + 9/20-1/4+...+85/400-1/80 =

1/5 + (7-5)/10 + (8-5)/15 +

   + (9-5)/20+ ... +(85 -5)/400 =

1/5 +2/5*2 +3/5*3 +4/5*4+...+80/5*80 =

1/5 +1/5(2/1 +3/3 +4/4 +...+80/80) =

1/5 + 1/5(1+1+1+...+1) =

1/5 +1/5*79 =

80/5 = 16

Targoviste44id

[tex]\dfrac{1}{5}+\dfrac{7}{10}+\dfrac{8}{15}+\dfrac{9}{20}+\ ...\ +\dfrac{85}{400}=\dfrac{1}{5}+\Big[(\dfrac{1}{5}+\dfrac{1}{2})+(\dfrac{1}{5}+\dfrac{1}{3})+(\dfrac{1}{5}+\dfrac{1}{4})+\ ...\ +(\dfrac{1}{5}+\dfrac{1}{80})\Big]=\\ \\ \\ =\dfrac{1}{5}+\dfrac{79}{5}+\Big(\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{4}+\ ...\ +\dfrac{1}{80}\Big)=16+\Big(\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{4}+\ ...\ +\dfrac{1}{80}\Big)[/tex]

[tex]a=16+\Big(\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{4}+\ ...\ +\dfrac{1}{80}\Big)-\Big(\dfrac{1}{2}+\dfrac{1}{3}+\dfrac{1}{4}+\ ...\ +\dfrac{1}{80}\Big)=16=4^2[/tex]

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