Răspuns:
Explicație pas cu pas:
a) 5 + 10 + 15 + ... +200 = 5*(1 + 2 + 3 + ...+ 40) = 5*40*41/2 = 5*20*41 = 4100
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b) 30 + 60 +90 + ... + 360 = 30*(1 + 2 + 3 + ...+ 12) = 30*12*13/2 = 2340
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c) 12*17 + 12*18 + 12*19 + ... + 12*86 = 12*(17 + 18 + 19 + ...+ 86)
17 + 18 + 19 + ... + 86 = 1 + 2 + 3 + ...+ 86 - (1 + 2 + 3 + ...+ 16)
= 86*87/2 - 16*17/2 = 3741 - 136 = 3605
12*3605 = 43260
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d) 99*98 - 98*97 + 97*96 - 96*95 + ... + 3*2 - 2*1
= 98*(99 - 97) + 96*(97 - 95) + ...+ 2*(3 - 1)
= 98*2 + 96*2 + ...+ 2*2
= 2*(98 + 96 + ... + 2)
= 2*2*(49 + 48 + ... + 1)
= 2*2*49*50/2 = 2*49*50 = 4900
