Question

A=1+2+3+.......+15
B=10+20+30+........150
C=1000+2000+3000+.........+15000

Aratati ca A+B+C este divizibil cu 90


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Answer 1

A = 1 + 2 + 3 + 4 + ...... + 15

A = 15 × ( 1 + 15 ) : 2

A = 15 × 8

A = 120

____________

B = 10 + 20 + 30 + ....... + 150

B = 10 × ( 1 + 2 + 3 + 4 +....... + 15 )

B = 10 ×  120

B = 1 200

_____________

C = 1 000 + 2 000 + 3 000 + ....... + 15 000

C = 1 000 × ( 1 + 2 + 3 + ....... + 15 )

C = 1 000 × 120

C = 120 000

____________

A + B + C = 120 + 1 200 + 120 000

A + B + C  = 121 320  

121 320 : 90 = 1 348

A + B + C = 1 348 × 90 → divizibil cu 90