Răspuns :

Danboghiu66id

S1 = 1+3+5+...+2019 = (1 + 2019) * n / 2

n = (2019 - 1) / 2 + 1 = 2018 /2 + 1 = 1009 + 1 = 1010

S1 = 2020 * 1010 / 2 = 1010^2

S2 = 1+3+5+...+1009 = (1 + 1009) m / 2

m = (1009 - 1) / 2 + 1 = 1008 / 2 + 1 = 504 + 1 = 505

S2 = 1010 * 505 / 2 = 505^2

a = rad(S1 / S2) = rad(1010^2 / 505^2) = 1010 / 505 = 2

a=2 este numarul natural cautat

Răspuns:

Explicație pas cu pas:

1 + 3 + 5 + ..... + 2019

a1 = 1; an = 2019; r = 2

an = a1 + (n - 1)r

2019 = 1 + (n - 1)*2 = 1 + 2n - 2 = 2n - 1

2n = 2019 + 1 = 2020

n = 2020 : 2 = 1010

Sn = n(a1 + an)/2 = 1010 (1 + 2019)/2 = 1010*2020/2 = 1010*1010

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1 + 3 + 5 + ..... + 1009

a1 = 1; an = 1009; r = 2

an = a1 + (n - 1)r

1009 = 1 + (n - 1)*2 = 1 + 2n - 2 = 2n - 1

2n = 1009 + 1 = 1010

n = 1010 : 2 = 505

Sn = n(a1 + an)/2 = 505 (1 + 1009)/2 = 505*1010/2 = 505*505

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1010*1010/505*505 = 4

a = √4 = 2, numar natural

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