Question

,
а) тт.
Calculaţi, după modelul potrivit, suma tuturor numerelor naturale consecu-
tive:
a) mai mici decît 11;
b) mai mici decît 16;
c) mai mici sau egale cu 20; d) mai mici sau egale cu 31.
Modele:
0+1+2+3+4+5+6 =
=(1+6) +(2+5)+(3+4) =
= 7+7+7=
= 3x7=21
0+1+2+3+4+5+6+7=
= (1+7)+(2+6)+(3+5)+4 =
=8+8+8+4=
= 3x8+4= 28​

Answer 1

Răspuns:

a)0+1+2+3+4+5+6+7+8+9+10+11=(0+11)+(1+10)+(2+9)+(3+8)+(4+7)+(5+6)=11+11+11+11+11+11=66

b)0+1+2+3+4+5+6+7+8+9+10+11+12+13+14+15+16=(0+16)+(1+15)+(2+14)+(3+13)+(4+12)+(5+11)+(6+10)+(7+9)+(8+8)=16+16+16+16+16+16+16+16+16=144

c)0+1+2+3+4+5+6+7+8+9+10+11+12+13+15+16+17+18+19+20=(0+20)+(1+19)+(2+18)+(3+17)+(4+16)+(5+15)+(6+14)+(7+13)+(8+12)+(9+11)+10=20+20+20+20+20+20+20+20+20+20+10=210

d)0+1+2+3+4+5+6+7+8+9+10+11+12+13+14+15+16+17+18+19+20+21+22+23+24+25+26+27+28+29+30+31=(0+31)+(1+30)+(2+29)+(3+28)+(4+27)+(5+26)+(6+25)+(7+24)+(8+23)+(9+22)+(10+21)+(11+20)+(12+19)+(13+18)+(14+17)+(15+16)=31*16=496