Question

cat este S=1+2+3+....+18+19+20​

Answer 1

Folosim formula Sn=[(a1+an)*n)]/2

S=[(1+20)*20]/2 = 21*10 = 210

Answer 2

Varianta 1:

Folosesti suma lui Gauss  : 1+2+3+...+n=n(n+1)/2 , unde n∈|N*

S=1+2+3+...+18+19+20=20·21/2=10·21=210

Varianta 2:

Grupezi termenii intr-un mod convenabil:

S=1+2+3+...+20

S=(20+1) + (19+2) + (18+3) + ... + (11+10)  (in total sunt 20:2=10 paranteze)

S=21+21+21+...+21 ( de 10 ori 21)

S=21·10

S=210

Varianta 3:

Presupunand ca nu stii suma lui  Gauss, poti folosi metoda aceasta.

(Asa s-a demonstrat ca 1+2+3+...+n=n(n+1)/2 )

S=  1 + 2 + 3+...+18+19+20

S=20+19+18+....+3 + 2 + 1

-------------------------------------- +

2S=(20+1) +(2+19)+(3+18)+...+(20+1)  ( in total avem 20 de paranteze)

2S=21·20

S=21·20/2

S=21·10

S=210