Question

Se consideră numerele x=1+2+3+...+20 y=2+4+6+...+40 si z=3+6+9+...+60
arata ca x=210
calculeaza x+y+z​

Answer 1

x = 1 + 2 + 3 + ... + 20 = 20*21 /2 ( Suma Gauss)

= 420 / 2 = 210

-> x = 210

y = 2 + 4 + 6 + .... + 40 = 2( 1 + 2 + 3 + .... + 20) = 2 * 210

z = 3 + 6 + 9 + ...... + 60 = 3( 1 + 2 + 3 + ... + 20 ) = 3 * 210

x + y + z = 210 + 2 * 210 + 3 * 210 = 210 * ( 1 + 2 + 3) = 210 *6 = 1260