Question

1.Calculati sumele pare consecutive pana la :42, 28
2.calculati sumele impare consecutive pana la: 89, 79

Answer 1

1.
2+4+6+8+...+42
dam factor comun pe 2
=2(1+2+3+..+21)
aplicam suma lui gaos s=n(n+1)/2
s=2*21(21+1)/2=2*21*22/2=21*22=462

2+4+6+...+28=2(1+2+3+...+14)
s=2*14(14+1)/2=14*15=210

2.
1+3+5+...+89
introducem numerele pare intre ele si le scadem dupa
1+2+3+...+89-(2+4+6+8+...+88)
paranteza o calculam separat
2+4+6+..+88=2(1+2+3+...+44)=2*44*45/2=1980
1+2+3+...+89=89*90/2=4005
si facem diferenta
4005-1980=2025

1+3+5+...+79
1+2+3+..+78+79-(2+4+6+...+78)=1+2+3+...+79-2(1+2+3+...+39)=79(79+1)/2-2*39(39+1)/2=
=79*80/2-2*39*40/2
=3160-1560=1600