Question

calculați după model suma Gauss a) 1+2+3+...+98+99+100 b)1+2+3+...+998+999+1000 c)101+102+103+...+998+999+1000

Answer 1

a: (1+100)×100:2=101×50=5050
b: (1+1000)×1000:2=1001×500=500500
c: (101+1000)×899:2=1101×899:2=989799:2=494899,5

Answer 2

a) 1+2+3+...+98+99+100 = [100 × (100+1)]:2= 5050

b)1+2+3+...+998+999+1000 =[1000 × (1000+1)]:2= 500500

c)101+102+103+...+998+999+1000 =S

S =S1 - S2 unde  S1 =1+2+3+...+998+999+1000   iar S2 = 1+2+3+...+98+99+100

S = S1 - S2 = 500500 - 5050 = 495450l

S1 si S2 au fost calculate la subpunctele a) respectiv b)