Question

Calculati: (51+102+153+............+2601) :3 (3+6+9+...............+153).
[Suma lui Gauss]

Answer 1

(51+102+153+............+2601) :3 
=51*(1+2+3+...+51):3
$=17* \frac{51*(51+1)}{2} =17* \frac{51*52}{2} =17*1326=22542$

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(3+6+9+...............+153)=
$=3*(1+2+3+...+51$
$= 3*\frac{51*(51+1)}{2} =3* \frac{51*52}{2} =3*1326=3978$

Answer 2

51(1+2+3+....+51):3(1+2+3+...+51)=51*25perechi*54suma unei perechi+26 nr. fara pereche :3*idem ,prima paranteza =51*1:3  =17