Question

1/2+2/2+....+20/2+21/2=

Answer 1

1/2 + 2/2 + ... + 20/2 + 21/2 =

= (1 + 2 + ... + 20 + 21)/2

Observam ca la numarator avem o suma de tip Gauss si o calculam cu ajutorul formulei

1 + 2 + ... + n = n·(n + 1) : 2

= (21×22 : 2)/2

= (21×11)/2

= 231/2

Answer 2

1 / 2 + 2 / 2 + .... + 20 / 2 + 21 / 2 =

( 1 + 2 + .... + 20 + 21 ) / 2 =

( 21 × 22 : 2 ) / 2 =

( 462 : 2 ) / 2 =

231 / 2