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a fost răspuns

Calculati media aritmetica a numerelor a si b unde a este cel mai mare divizor comun al numerelor 25 si 105, iar b=

[tex] \frac{1}{1 \times 2} + \frac{1}{2 \times 3} + \frac{1}{3 \times 4} + \frac{1}{4 \times 5} [/tex]
Mulțumesc!​

Răspuns :

a=(25,105)

25=5²

105=3×5×7

(25,105)=5

a=5

b=1/(1×2)+1/(2×3)+1/(3×4)+1/(4×5)

b=1/1×1/2+1/2×1/3+1/3×1/4+1/4×1/5

b=1/2×(1/1+1/3)+1/4×(1/3+1/5)

b=1/2×(3/3+1/3)+1/4×(5/15+3/15)

b=1/2×4/3+1/4×8/15

b=2/3+2/15

b=10/15+2/15

b=12/15

b=4/5

mₐ=(a+b)/2

mₐ=(5+4/5)/2

mₐ=(25/5+4/5)/2

mₐ=29/5/2

mₐ=29/5×1/2

mₐ=29/10

Răspuns:

Explicație pas cu pas:

25 = 5^2

105 = 3*5*7

cmmdc (25, 105) = 5

a = 5

________

1/2 + 1/6 + 1/12 + 1/20 = 6/12 + 2/12 + 1/12 + 1/20 = 9/12 + 1/20 = 3/4 + 1/20

= 15/20 + 1/20 = 16/20 = 4/5

b = 4/5

__________

Ma = (a + b) : 2

a + b = 5 + 4/5 = 25/5 + 4/5 = 29/5

Ma = 29/5 : 2 = 29/10 = 2,9

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