Question

Demonstreaza ca nr a este patrat perfect , unde a=1+2+3+...+101+51*101 dau coroana

Answer 1

1+2+3+...+100=100x101:2=50x101
Ne  bazam pe teoria Suma=n(n+1):2
a=1+2+3+...+100+51x101=50x101+51x101(cum am explicat mai sus)==>101(51+50)=101x101=101 la patrat deci e patrat perfect :)

Answer 2

a=1+2+3+...+101+51·101
a=101·102/2+51·101
a=101·51+51·101
a=[101+51]²⇒a este patrat perfect;