Question

1. Aratati ca urmatoarele numere sunt patrate perfecte:
a) a=(1+2+3+...+15)+1
b) b=2*(1+2+3+...+100)+101
c) c=2013+2012*2013
d) d=2011*2012-2011
2. Aratati ca urmatoarele numele sunt cuburi perfecte:
a) a=8+2*(1+2+3+...+7)
b) b=2*(1+2+3+...+63) +64
c) d=2*(1+2+3+...+999)+1000

Answer 1

a. [(1+15)*15]: 2+1= [16*15]:2+1= 240:2+1 120+1= 121 b.2*[(1+100)*100]:2+101= 2*[101*100]:2+101= 2*10100:2+101= 20200:2+101= 10100+101= 10201 c.216+2*[(1+215)*215]:2 =216+2*(216*215):2 =216+2*46440:2 =216+92880:2 =216+46440 =46656 d. 4046132-2011 =4044121