Question

Va rog ajutați-mă!
a) 10+20+30+......500=
b) 7+14+21+28+.....217=
c) 1+2+3+4+.....10+x=3000
Urgent vă rog! Mulțumesc!

Answer 1

a) 10+20+30+......500 = 10·( 1+2+3+....+50) = 10 ·[50·(50+1)]:2 = 5·50·51 = 12750

b) 7 + 14+21+28+.....217 = 7 · (1+2+3+......31) = 7 ·[31·(31+1)]:2=7·31·32:2 = 3472

c) 1 + 2 + 3 + 4+.....10 + x = 3000 ⇒ x = 3000 - (1 + 2 + 3 + 4+.....10) ⇒ x =3000 - [(10·(10+1)]:2=

= 3000 - 55 = 2945

Answer 2

a) 10+20+ .. + 500 =

= 10·( 1+2+ ...+50)

= 10·50·51 : 2

= 12750

b) 7 + 14 + 21 + .. + 217 =

= 7·(1 + 2 + .. + 31)

= 7·31·32 : 2

= 3472

c) 1 + 2 + .. + 10 + x = 3000

x = 3000 - (1 + 2 + .. + 10)

x =3000 - 10·11 : 2

x = 3000 - 55

x = 2945