A) Efectuati: (12+24+36 ... +444):(6+12+18 ... +222)
b) Calculati: (4+8+12 ... +2.012):(2+4+6 ... +1.006)
c) Determinati: 6+11+16+21+ ... +506
d) Efectuati: 4+9+14+19+ ... +1.004
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Răspunsuri la întrebare
Răspuns:
a( (12+24+36 ... +444):(6+12+18 ... +222)
12*(1+2++...+37)/6(1+2+3+...+37)=12*(37*38/2)/6*(37*38/2)=12/6=2
b)(4+8+12+....+2012)/(2+4+6+....+1006)
2*(1+2+3+...+1006)/2*(1+2+...+503)=(2*1006*1007/2)/(2·503·504/2)=
1013042/253512=4
c) 6+11+16+21+ ... +506
6=1+5·1 11=1+5·2 16=1+5·3 ........... 506= 1+5·101
S = 1*101 + 5(1+2+3+.......+101)= 101+5*(101*102/2) = 101+25755 = 25856
d) 4+9+14+19+ ... +1.004
4=4+5*0 9=4+5*1 14=4+5*2 ......... 1004=4+5*200
S=4*200+5*(200*201/2)=804+100500=101300
Explicație pas cu pas:
(12 + 24 + .. + 444) : (6 + 12 + .. + 222) =
= 12(1 + 2 + .. + 37) : 6(1 + 2 + .. + 37)
= 12 : 6
= 2
(4 + 8 + .. + 2012) : (2 + 4 + .. + 1006) =
= 4(1 + 2 + .. + 503) : 2(1 + 2 + .. + 503)
= 4 : 2
= 2
6 + 11 + .. + 506 =
= (1 + 5·1) + (1 + 5·2) + .. + (1 + 5·101)
= 101 + 5(1 + 2 + .. + 101)
= 5×101×102 : 2 + 101
= 25755 + 101
= 25856
4 + 9 + .. + 1004 =
= (4 + 5·0) + (4 + 5·1) + .. + (4 + 5·200)
= 4·201 + 5(1 + 2 + .. + 200)
= 804 + 5·200·201 : 2
= 804 + 100500
= 101304