Question

A)2+3+4+...+50
B)1+2+3+...+500
C)1+97+2+999+3+198
D)l+2+3+...+124
E)2+4+6+...+600
F)15+16+17+...+70
G)5+6+7+...+81
H)1+2+3+...+512
I)317+318+319+...+400
Dau coroana+5 stele!!

Answer 1

Răspuns:

A)2+3+4+5+...50= 1+2+3+4+5...50-1 = (50*51)/2-1= 1275-1= 1274

B 1+2+3+...500 = suma lui gaus clasica n*(n+1)/2= (500*501)/2= 125250

C 1+97+2+999+3+198= 1301

D 1+2+3+...124= (124+125)/2= 7750

E 2+4+6+....600

scoatem 2 in factur si avem 2(1+2+3+...300)

deci in paranteza suma lui gaus  si avem 2x(300*301)/2= 300+301= 90300

F 15+16+17+...70

ADUNAM 1+2+3...14 SI SCADEM 1+2+3+...14

obtinem 1+2+3...70-(1+2+3....14)

sume a lui gaus  si avem (70*71)/2- (14*15)/2= 2485-105= 2380

h 1+2+3...+512= (512*513)/2= 131328

I 317+318+319....+400  ADUNAM 1+2+3+.....316 SI APOI SCADEM1+2+3.....316

AVEM 1+2+3+,,,,,400- (1+2+3+.....316) = (400*401)/2-(316*317)/2= 80200-50086= 30114