Question

5.Arătați că
h.30^n|Sa stiti ca e bara(5^n•6^n+15^n•2^n+1)
j.50500trei puncte (1+2+3+...+100)
i.27540trei puncte(1^2+2^2+3^2+4^2)
k.21|(1+2+3+...+20
Va rog sa ma ajute cineva repede ca dau coroana si 90 de puncte va rog repede ​

Answer 1

Răspuns:

h.30^n | (5^n•6^n+15^n•2^n+1)

30ⁿ I (5·6)ⁿ+(15·2)ⁿ·2

30ⁿ I 30ⁿ+30ⁿ×2

30ⁿ I 30ⁿ(1+2)

30ⁿ I 30ⁿ×3

_______________

50500⋮ (1+2+3+...+100)

1+2+3+..+100=(100·101)/2=5050

50500⋮5050

_____________

27540 ⋮ (1^2+2^2+3^2+4^2)

1^2+2^2+3^2+4^2=1+4+9+16=30

27540 ⋮ 30

________________

21 | (1+2+3+...+20)

1+2+3+...+20=20×21/2=210

21 I 210