Question

1+3+5+...+99+x=2+4+6+...+100

Answer 1

Răspuns:

Explicație pas cu pas:

1+3+5+...+99+x = 2+4+6+...+100  <=>

1+3+5+...+99+x = (x+1)·[(x-1):2+1]:2

2+4+6+.....+100 = (2+100)·[(100-2):2 +1]:2 = 102·50:2 = 102·25 = 2550

1+3+5+...+99 = (1+99)·[(99-1):2+1]:2 = 100·50:2 = 50·50 = 2500

=> 2500 + x = 2550 => x = 2550-2500 => x = 50