Question

Valoarea lu x din proporția 1+2+3+...+100/25=x/3 est: a)101 b)100 c)606 d)51.repede am nevoie!!!!dau coaroana

Answer 1

Formula lui Gauss

1+2+3+...+n = n(n+1)/2

1+2+3+...+100/25=x/3

Avem

100×101/2/25 = x/3

50×101/25 = x/3

2×101 = x/3

x/3=202

x= 202×3= 606

Explicație pas cu pas:

Answer 2

$\it 1+2+3+...+ 100=\dfrac{100\cdot101}{2}=50\cdot101$

Proporția devine:

$\it \dfrac{50\cdot101^{(25}}{25}=\dfrac{x}{3} \Rightarrow 2\cdot101=\dfrac{x}{3} \Rightarrow x=3\cdot2\cdot101 \Rightarrow x = 606$