Question

a) 1+4+7+10+....+139
b) 2000+2001+2002+...+2010.
Va rog frumoss! Urgent!!

Answer 1

a) 1 = 3*0 + 1 ;
    4 = 3*1 + 1 ;
    7 = 3*2 + 1 ;
   10 = 3*3 + 1 ;
.........................
   139 = 3*46 + 1 ;
_________________
S = 3( 1 + 2 + 3 + ... + 46 ) + 47 ;
Aplici suma lui Gauss ; obtii ca S = 3 * 46*47 / 2 + 47 => S = 3*23*47 + 47 =>
S = 70*47 => S = 3290 ;

b) S = 2000 + ( 2000 + 1 ) + ( 2000 + 2 )  + .... + ( 2000 + 10 ) => S = 11*2010 + ( 1 + 2 + ... + 10 ) => S = 22110 + 10*11 / 2 => S = 22110 + 55 => S = 22165 ;

Bafta !