Question

Aflati suma tuturor numerelor naturale de forma abc bara sus, care impartite la un numar de o cifra , dau restul egal cu 8
Ajutor dau coroana

Answer 1

Poza conține rezolvarea.

Answer 2

abc : n = c rest 8

n = numar de o cifra

n > 8
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=> n = 9

abc = 9 × c + 8

abc = M9 + 8 ; 90 < M9 < 1000

abc = 9 × 11 + 8 = 99 + 8 = 107 (cel mai mic numar de 3 cifre )
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abc = 9 × 110 + 8 = 990 + 8 = 998 (cel mai mare numar de 3 cifre)
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S =( 9 × 11 + 8 ) + (9 × 12 + 8) +...+ (9 × 110 + 8)

S = 9 × (11 + 12 +...+ 110) + (8 + 8+...+8 de 100 de ori)
S = 9 ×{ [1+2+...+110 - (1+2+..+10)}+ 8 × 100

S = 9 × (110 × 111 : 2 - 10×11 : 2) + 800

S = 9 × (55 × 111 - 55) + 800

S = 9 × 55 × (111 - 1) + 800

S = 495 × 110 + 800

S = 54 450 + 800

S = 55 250 (suma)
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