Question

1+2+...+18=
Vreau rezolvarea prin asocierea nr.

Answer 1

1+2+3+4+5+6+7+8+9+10+11+12+13+14+15+16+17+18=171

Answer 2

S =  1 + 2   + 3 + .....  + 17 + 18

S = 18 + 17 + 16  + ...... + 2 + 1

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2 x S = ( 1 + 18 ) + ( 2 + 17 ) + ( 3 + 16 ) + ........ ( 17 + 2 ) + ( 18 + 1 )

       S =  19 × (18 termeni : 2) sume

       S = 19 × 9

       S = 171  

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sau:  

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

= 19 + 19 + 19 + 19 + 19 + 19 + 19 + 19 + 19 =

= 171