Question

1+2+3+...+150

244+6+...+200

1+3+5+...+101

10+12+14+...+420

VA ROG EU NU DATI SEEN E URGENT​​

Answer 1

Răspuns:

Explicație pas cu pas:

1 + 2 + 3 + ...... + 150 = 11 375

= 150 × ( 1 + 150 ) : 2 =

= 150 × 151 : 2 =

= 22 650 : 2 =

= 11 375

________________________

2 + 4 + 6 + ...... + 200 = 10 100

= 2×1 + 2×2 + 2×3 + ........ + 2×100 =

→ îl dau factor comun pe 2

= 2 × ( 1+2+3+.......+100) =

= 2 × 100 × ( 1+100) : 2 =

= 100 × 101 =

= 10 100

______________________

1+3+5+.......+101 = 2 601

(101 - 1 ) : 2 + 1 = 100 : 2 + 1 = 51 termeni impari are suma

= 51 × ( 1+101) : 2 =

= 51 × 102 : 2 =

= 51 × 51 =

= 2 601

________________________

10+12+14+.....+420 =

= 2×5+2×6+2×7+......+ 2×210 =

= 2 × ( 5+6+7+.........+210) =44 290

210 - 5 + 1 = 206 termeni are suma parantezei rotunde

= 2 × 206 × ( 5+210) : 2 =

= 206 × 215 =

= 44 290

__________________________

5+6+7+......+210 =suma parantezei

adaug primele 4 numere nenule, apoi le scad

= (1+2+3+4+5+6+7+......+210) - (1+2+3+4) =

= 210 × (1+210 ) : 2 - 10 =

= 105 × 211 : 2 - 10 =

= 22 155 - 10 =

= 22 145