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a fost răspuns

cum se rezolva 9+10+11+...+30

Răspuns :

Cocirmariadenis

9 + 10 + 11 + ...... + 30 = ( 30 - 9 + 1 ) termeni × ( 9 + 30 ) : 2 = 429

= 22 × 39 : 2 =

= 11 × 39 =

= 429

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S = 9 + 10 + 11 + 12 + 13 + 14 + 15 + 16 + ...... + 30

S = 30 + 29 + 28 + ........................................+  9

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2 x S = ( 9 + 30 ) + ( 10 + 29 ) + ( 11 + 28 ) + ....... + ( 30 + 9 )

→ stabilesc cati termeni are suma: 30 - 9 + 1 = 22 termeni

S = 22 × 39 : 2

S = 858 : 2

S = 429


Mikelina

Aplicăm formula:

S=(a1+an)×n/2

a1=primul termen

an=ultimul termen

n =nr termenilor

n=an-a1+1=30-9+1=22

S=(9+30)×22/2=39×11=429

Alt mod de rezolvare:

S=n[(n+1)/2)]

9+10+11+....+30=

(1+2+3...+30)-(1+2+3+...+8)=

(30×31):2-(8×9):2=

15×31-4×9=

465-36=

429