Question

Calculati :

a)  3 + 6 + 9 + 12 + . . . + 2001 ;
b ) 4 + 8 + 12 + . . .  + 2000 ;
c ) 5 + 10 + 15 + . . . + 2000 ;
d ) 7 + 14 + 21 + . . . + 2002 ;

Answer 1

a) 3 + 6 + 9 + 12 +.........+ 2001 = 3(1 + 2 + 3 + 4 +....+ 667) = 3 * 667 * (667 + 1)/2 = 2001 * 668/2 = 2001 * 334 = 668 334
b) 4 + 8 + 12 + .+ 2000 = 4*(1 + 2 + 3 +.....+ 250) = 4 * 250/2 * (250 + 1) = 500 * 251 = 
125 500
c) 5 + 10 + 15 + ....+ 2000 = 5(1 + 2 + 3 + ....+ 400) = 5 * (400 + 1) * 400/2 = 5 * 401 * 200 = 401 000
d) 7 + 14 + 21 + .... + 2002 = 7(1 + 2 + 3 + ....+ 286) = 7 * 286/2 * ( 286 + 1) = 7 * 143 * 287 = 287 287