Question

a) Determinați :
6+11+16+21+...+506

b) Efectuați :
4+9+14+19+...+1004

Answer 1

Răspuns:

6 + (6+1·5)+(6+2·5)+(6+3·5)+ ... +(6+100·5) =

101·6+5·(1+2+3+...+100)=

101·6+5·(100·101)/2 =

101(6+5·50)=101(6+250)=

101·256=25856

______________

4+9+14+19+....+1004=

4+(4+5)+(4+2·5)+(4+3·5)+....+(4+200·5)=

4·201+5(1+2+...+200)=

4·201+5·200·201/2=

4·201+500·201=

201(4+500)=

201·504=101304