Question

a.Care sunt numerele impare cuprinse intre 100 si 564 ?
b. calculati suma acestor numere naturale impare .

Answer 1

a. Numerele impare sunt:101,103,105,107,109,.....,563;
b. S=101+103+105+...+561+563=[1+2+3+...+563]-[1+2+3+....+100]-[102+104+...+562]=[563·564/2]-[100·101/2]-2[51+52+...+281]
⇒[563·282]-[50·101]-2[[1+2+3+....+281]-[1+2+3+....+51]]
⇒158766-5050-2[[281·282/2]-[51·52/2]]
⇒153716-2[[281·141]-[51·26]]
⇒153716-2[39621-1326]
⇒153716-2·38295
⇒153716-76590
⇒77126;⇒S=77126;