Question

daca a= ½+⅓+¼+....+¹/53 si b=½+⅔+¾+...+52/53. calculati media aritmetic a nr a si b

Answer 1

Media aritmetica = suma nr /2. a+b=1/2+1/2+1/3+2/3+....1/53+52/53. (Am luat un termen de la un nr si un termen de la celalalt nr)Grupanad termenii cate 2 observam sa suma se reduce la a+b=1+1+1+.. 1. Avem 52 de termeni1=>a=b=52 =>Ma=52/2=26

Answer 2

a= [tex]\frac{1}{2} + \frac{1}{3} + \frac{1}{4}+.....+ \frac{1}{53} [/tex]
b= $\frac{1}{2} + \frac{2}{3} + \frac{3}{4}+......+ \frac{52}{53}$
ma= $\frac{( \frac{1}{2}+ \frac{1}{2} )+( \frac{1}{3}+ \frac{2}{3})+...( \frac{1}{53}+ \frac{52}{53}) }{2}$
ma= $\frac{ \frac{2}{2}+ \frac{3}{3}+ \frac{4}{4}+...+ \frac{53}{53} }{2$
ma= $\frac{1+1+1+....+1 }{2}$   (1 de 52 de ori)
ma= $\frac{52}{2}$ =26