Question

aflati nr x care verifica egalitatea 1 + 3 + 5 +...+ 99 + x = 2 + 6 +...+  100

Answer 1

(1 + 99)/2 * 99 + x = (2 + 100)/2 * 100
50 * 99 + x = 51 * 100
x = 5100 - 4950
x = 150

Answer 2

S1 = 1+3+5+7+......+99    S2 = 2(1+3+5+.........+49+50 )

S1 = (1+99)·25 = 2500  

1 = 1 +2·0

3 = 1+ 2·1

5 = 1 +2·2

............

49 = 1 + 2·24 ⇒ S2 =2·[1·25 +2(1+2+3+....+24) ]+100 = 50 + 2·24·25 +100  = 1350

....99=1+ 2·49 ⇒S1= 1·50 + 2(1+2+3+....+49) =50+49·50=2500

2500 + x = 1350  ⇒ x= - 1150