Question

Sa se calculeze suma :

C = 4 + 9 + 14 + ........... + 104 + 109

( Suma lui Gauss )

( Rezolvare pentru clasa a IV - a )

Answer 1

C = 4 + 9 + 14 + .... + 104 + 109

c = 4 + ( 4 + 5 × 1 ) + ( 4 + 52 ) + ...( 4 + 5 × 20 )
+ ( 4 + 5 × 21 )

C = 4 × 22 + 5 × ( 1 + 2 + .....+ 20 + 21 )

C = 88 + 5 × S 21 = 88 + 5 × 21 × 22 supra 2

C = 88 + 5 × 231 = 88 + 1155

C = 1243

Answer 2

C = 4 + 9 + 14 + ........... + 104 + 109

C = 5×1-1 + 5×2-1 + 5×3-1 +...5×21-1 + 5×22-1

C = 5×(1 + 2 + 3 +...+ 21 + 22) - (1 + 1+ 1+...+1 de 22 de ori)

C = 5 × 22 × (22+1) : 2 - 1 × 22

C = 110 ×23 : 2 - 22

C = 55 × 23 - 22

C = 1 265 - 22

C = 1 243