Question

S =101 + 103 + 105 +… 199
Calculați folosind Suma Lui Gauss

Answer 1

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)

$1+2+3+4+...+100 = \frac{100*101}{2} = 50*101=5050$

$2(1+2+3+...+50) = 2*\frac{50*51}{2} = 50*51 = 2550$

T = 5050-2550=2500

S = 10000 + 2500 = 12500