Question

Aratati ca urmatorul numar este patrat perfect :a=(1+2+3+......+99)X2+100

Answer 1

$a=(1+2+3+..+99)*2+100 \\ a = \frac{99*100}{2}*2+100=99*100+100 = 100(99+1) = 100*100$
=> a -> este  patrat perfect.

Answer 2

1ori 99 ori 100 imparit la 2 ori 2 plus 1009900 impartit la 2 ori 2 plus 1004950 ori 2 plus 100 9900 plus 100 =10000