Question

calculati urmatoarele sume : a) 1+2+3+....+80 , b) 2+4+6+...+100 , c)1+3+5+...+99 ,d)3+7+11+15+...43

Answer 1

a)   1 + 2 + 3 + ..... + 80 = 80 × ( 1 + 80 ) : 2 = 80 × 81 : 2 = 3 240

b)   2 + 4 + 6 + ...... + 100 = 2 × ( 1 + 2 + 3 + ....... + 50 ) = 2 × 50 × 51 : 2 = 2 550

c)   1 + 3 + 5 + ...... + 99 =

→ stabilesc cati termeni are suma cu ratia = 2 ( 3 - 1 = 2;   5 - 3 = 2;..... )

( 99 - 1 ) : 2 + 1 = 50 termeni are suma

= 50 × ( 1 + 99 ) / 2 =

= 50 × 50 =

= 2 500

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d )  S = 3 + 7 + 11 + 15 + ....... + 43

→ stabilesc cati termeni are suma cu ratia = 4 ( 7 - 3= 4;    11 - 7 = 4;.... )

( 43 - 3 ) : 4 + 1 = 11  termeni are suma

→ aplic formula sumei lui Gauss

S = 11 × ( 3 + 43 ) : 2

S = 11 × 46 : 2

S = 11 × 23

S = 253