Question

calculati 64+63+62+.......33+32

Answer 1

S=32+33+...+62+63+64 / + (1+2+3+4+5+...+31) => S + (1+2+3+4+...+31) = 1+2+3+4+5+...+64=> S + (31*32)/2=(64*65)/2 => S+496 =2080 => S=1584
Suma lui Gauss : 1+2+3+4+5+...+n= n(n+1) supra 2

Answer 2

Cu Sume Gauss:
32+33+...+62+63+64= 1+2+3+...+63+64-(1+2+...+30+31)=64(64+1)/2-31(31+1)/2=64·65/2-31·32/2=32·65-31·16=16(2·65-31)=16(130-31)=16·99=1584