Question

sa se afle y din ecuatia 1000y+2+4+6...+2002egal1001*2002

Answer 1

1000y+2 x (1+2+...+1001)=1001 x 2002
1000y+2 x 1001 x 1002 : 2 = 1001 x 2002
1000y+1001 x 1002 = 1001 x 2002
1000y = 1001 x (2002 - 1002)
1000y = 1001 x 1000
y = 1001

Answer 2

2 + 4 + 6 +...+ 2002 = 2(1+2+3+ ... +1001) =2·(1001·1002)/2 = 1001·1002

Acum, ecuația se scrie:

1000y +1001·1002 =1001·2002 ⇒ 1000y = 1001·2002 -1001·1002 ⇒

⇒ 1000y =  1001(2002 - 1002) ⇒ 1000y =1001·1000|:1000 ⇒y = 1001  .