Question

2.efectuati:
100+200+300+....+1200-25-50-75-....-300
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Answer 1

Răspuns:

Explicație pas cu pas:

Notez S=100+200+300+....+1200-25-50-75-....-300

S=100+200+300+....+1200-25-50-75-....-300=

=100·(1+2+3+...+12)-25·(1+2+3+...+12)=(100-25)·(1+2+3+...+12)=75·(1+2+3+...+12) =>

S/75=1+2+3+...+10+11+12

S/75=12+11+10+...+3+2+1

2·S/75=(1+12)+(2+11)+(3+10)+...+(10+3)+(11+2)+(12+1) =>

2·S/75=13+13+13+...+13+13+13=13·12 => S=13·12·75/2=13·6·75=5850