Raspuns :
S = 12500
Explicatie :
S = 100 + 100 + 100 + .... + 100 + 1 + 3 + 5 + ... + 99
S = 100*100 + 1 + 3 + 5 + ... 99
Fie T = 1 + 3 + 5 + ... 99
T = 1+2+3+4+...+100 - (2+4+6+8+...+100)
T = 1+2+3+4+...+100 - 2(1+2+3+...+50)
[tex]1+2+3+4+...+100 = \frac{100*101}{2} = 50*101=5050[/tex]
[tex]2(1+2+3+...+50) = 2*\frac{50*51}{2} = 50*51 = 2550[/tex]
T = 5050-2550=2500
S = 10000 + 2500 = 12500
