Calculati,dupa modelul potrivit,suma tuturor numerelor naturale consecutive: a)mai mici decit 11; b)mai mici decit 16 c)mai mici sau egale cu 20 d)mai mici sau egale cu 31

a) 1+2+3+.....+10=

=10*(10+1):2=

=10*11:2=

=110:2=

=55

b) 1+2+3+.....+15=

=15*(15+1):2=

=15*16:2=

=240:2=

=120

c) 1+2+3+.....20=

=20*(20+1):2=

=20*21:2=

=420:2=

=210

d) 1+2+3+....31=

=31*(31+1):2=

=31*32:2=

=992:2=

=496

a)  S = 1 + 2 + 3 + 4 + .... + 10

S = 10 × ( 1 + 10 ) : 2

S = 10 × 11 : 2

S = 55

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b)   S = 1 + 2 + 3 + .... + 15

S = 15 × ( 1 + 15 ) : 2

S = 15 × 16 : 2

S = 15 × 8

S = 120

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c)    S = 1 + 2 + 3 + ....... + 20

S = 20 × ( 1 + 20 ) : 2

S = 10 × 21

S = 210

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d)  S = 1 + 2 + 3 + ...... + 31

S = 31 × ( 1 + 31 ) : 2

S = 31 × 32 : 2

S = 31 × 16

S = 496