Question

calculati a_(b_c),unde: a= 1+2+3...+2013,b=108+109+110+...+149, c= 13+14+15+...+42.

Answer 1

a = 1 + 2 + 3 + ...... + 2013

a = 2013 × ( 1 + 2013 ) / 4

a = 2013 × 2014 / 2

a = 2013 × 1007

a = 2 027 091

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b = 108 + 109 + 110 + ... + 149

→ stabilim cati termeni are suma : 149 - 108 + 1 = 42 termeni are suma

b = 42 × ( 108 + 149 ) / 2

b = 42 × 257 / 2

b = 21 × 257

b = 5 397

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c = 13 + 14 + 15 + .. . + 42

→ stabilim cati termeni are suma:   42 - 13 + 1 = 29 + 1 = 30 termeni

c = 30 × ( 13 + 42 ) / 2

c = 15 × 55

c = 825

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a - ( b - c ) = 2 027 091 - ( 5 397 - 825 ) = 2 027 091 - 4 572 = 2 022 519