Question

fie numerele m=1+3+5+...+99si n=13•(1+3+5+...+99).arata ca numărul m+n este divizibil cu 14

Answer 1

n•(n+1)/2=
m=99•(99+1)/2=
99•100/2=99•50=4.950
m=4.950
n=13•4950=64.350
m+n=64.350+4.950=69.300
69.300 nu se divide cu 14..

Answer 2

m=1+3+5+...+99=1+1x3+1x5+....+1x99
n=13x(1+3+5+...+99)=13+13x3+13x5+......+13x99
m+n=1+1x3+1x5+...+1x99  +  13+13x3+13x5+....+13x99
m+n=(1+13)+(1x3+13x3)+(1x5+13x5)+.....+(1x99+13x99)
m+n=14+14x3+14x5+....+14x99
m+n=14x(1+3+5+....+99)
deci m+n este divizibil cu 14