Question

calculati. 1+2+3+.........+49= 10+11+12 ...... +99=​

Answer 1

1+2+3+...+49=49×(1+49)/2=49×50/2= 49×100/4=4900/4=1225

Numarul de termeni: 49

10+11+....+99=90×(10+99)/2= 90×109/2=4905

Numar de termeni: 99-10+1=90

Answer 2

Răspuns:

Explicație pas cu pas:

1 + 2 + 3 + ..... + 49 = 1 225

→ aplic formula sumei lui Gauss

= 49 × ( 1 + 49 ) : 2 =

= 49 × 50 : 2 =

= 2 450 : 2 =

= 1 225

____________________________________

10 + 11 + 12 + ...... + 99 =

-> adaug si scad primi 9 termeni ai sumei

= ( 1 + 2 + 3 + .... + 9 + 10 + 11 + 12 + ..... + 99 ) - ( 1 + 2 + 3 + ..... + 9 ) =

= 99 × ( 1 + 99 ) : 2 - 9 × (1+9) : 2 =

= 99 × 100 : 2 - 90 : 2 =

= 9900 : 2 - 45 =

= 4950 - 45 =

= 4905

Sau:

10 + 11 + 12 + ... + 99 =

->  stabilesc cati termeni are suma:

99 - 10 + 1 = 89 + 1 = 90 termeni are suma

= 90 × ( 10 + 99 ) : 2 =

= 90 × 109 : 2 =

= 9 810 : 2 =

= 4 905