21+22+23+......+100 sume gauss

Răspuns :

100•101:2- 20•21:2=
101•50-10•21=
5050-210=4840

S = S₁ -S₂

Suma Gauss S =[n(n+1)]:2   unde n este ultimul termen al sumei

unde S₁ = 1 + 2 + 3+ .................+ 21 + 22 + 23 +......+ 100 = [100 ×(100+1)]:2=5050

S₂ = 1 + 2 + 3 +......+ 20 =[(20× (20+1)]:2= 210

S = S₁ -S₂ = 4840