Question

Calculati sumele

a)1+2+3+....+99+100
b)2+4+6+8+...+28
c)3+6+9+12+....+42+45
Urgent !!

Answer 1

Răspuns:

Explicație pas cu pas:

a)  1 + 2 + 3 + ..... + 99 + 100 = 5 050

= 100 × ( 1 + 100 ) : 2 =  → aplic formula sumei lui Gauss

= 50 × 101 =

= 5 050

__________________________________

b)  2 + 4 + 6 + ...... + 28 = 210

= 2 × ( 1 + 2 + 3 + ...... + 14 ) =

= 2 × 14 × ( 1 + 14 ) : 2 =

= 14 × 15 =

= 210

________________________

c)   3 + 6 + 9 + 12 + ...... + 42 + 45 = 360

= 3 × ( 1 + 2 + 3 + ..... + 14 + 15 ) =

= 3 × 15 × ( 1 + 15 ) : 2 =

= 45 × 16 : 2 =

= 45 × 8 =

= 360