Question

aratati ca urmatoarele numere sunt patrate perfecte
a=2003+2(1+2+...2002) ,
b=1+3+5 ... +2011,
c=82+2*81+3*81+...+49*81

Multumesc

Answer 1

 a = 2003 + 2(1 + 2 + ........ + 2002)
a = 2003 + 2 * 2002 * (2002 + 1)/2
a = 2003 + 2002 * 2003
a = 2003(1 + 2002)
a = 2003 * 2003
a = 2003²
b = 1 + 3 + 6 +.... + 2011
b = (2011 + 1)[(2011 - 1) : 2 + 1] : 2
b = 2012 * [2010 : 2 + 1] : 2
b = 2012 * 1006 : 2
b = 1006 * 1006
b = 1006²
c = 81 + 2 * 81 + 3 * 81 + .... + 49 * 81
c = 81(1 + 2 + 3 +.... + 49)
c = 81 * 49 * (49 + 1) : 2
c = 81 * 49 * 25
c = 9² * 7² * 5²
c = 315²