Question

c) 101+102+103+...+998+999+1000 suma Gauss

Answer 1

c)  S = 101 + 102 + 103 + ...... + 998 + 999 + 1 000

S = 1 000 + 999 + 998 + ......+103 + 102 +    101

____________________________________

2 × S = ( 101 + 1 000 ) + ( 102 + 999 ) + ....... + ( 999 + 102 ) + ( 1 000 + 101 )

2 × S = 1 101 + 1 101 + 1 101 + ......... + 1 101 + 1 101

____________________________________

→ stabilesc cati termeni are suma: 1 000 - 101 + 1 = 899 + 1 = 900 termeni are suma

→ sunt 900 de sume

_______________________________

2 × S = 900 × 1 101

S = 990 900 : 2

S = 495 450

__________________________

sau aplic formula sumei lui Gauss:

S = 900 × ( 101 + 1 000 ) : 2

S = 450 × 1 101

S = 495 450