Question

1+3+5+...47+49+51

1+3+5+...+67+69+71

1+3+5+...+111+113+115

​

Answer 1

Răspuns:

Explicație pas cu pas:

1+3+5+.....+47+49+51 =

(51-1) : 2 + 1 = 50 : 2 + 1 = 26 termeni impari consecutivi are suma, primul fiind 1

= 26 × (1+51) : 2 =

= 26 × 52 : 2 =

= 26 × 26 =

= 676

_________________________

Al doilea mod de rezolvare: adaug și numerele pare, pe care le scad apoi:

1+2+3+4+5+6+.....+49+50+51 - (2+4+6+.....+50) =

= 51 ×(1+51):2 - 2×(1+2+3+.....+25) =

= 51×52:2 - 2×25×(1+25): 2 =

= 51×26 - 25×26 =

= 26 × (51-25) =

= 26×26 =

= 676

_______________________________

1+3+5+.....+67+69+71 =

(71-1) : 2 + 1 = 70 : 2 + 1 = 36 termeni impari consecutivi are suma

= 36 × (1+71) : 2 =

= 36 × 72 : 2 =

= 36 × 36 =

= 1 296

_________________________

1+3+5+.....+111+113+115 =

(115-1) : 2 + 1 = 114 : 2 + 1 = 58 termeni impari are suma

= 58 × (1+115) : 2 =

= 58 × 116 : 2 =

= 58 × 58 =

= 3 364