Question

Aratati ca urmatoarele numere sunt patrate perfecte dupa care calculati radical din x.a*x=6+12+18+...+288.   B(x=4+8+12+....+196     C( x= 1+3_5_..+101 D*x=1+3+5+...+2011 E(x=1203+2+4+6+...+2404 Am nevoie urgenta daca se poate

Answer 1

x=6+12+18+...+288=6(1+2+...+48)=6*48*49:2=7056=84²√7056=√84²=84

x=4+8+12+....+196=4(1+2+3+...49)=4*49*50:2=4900=70²

√4900=√70²=70

x= 1+3+5+..+101=1+3+..+(2*50+1)=(50+1)²=51²


√51²=51

x=1+3+5+...+2011=x=1+3+5+...+(2*1005+1)=(1005+1)²=1006²

√1006²=1006



x=1203+2+4+6+...+2404=2+4+6+...+2404+1203=2(1+2+..+1202)+1203=2*1202*1203:2+1203=1202*1203+1203=1203(1202+1)=1203*1203=1203²

√1023²=1023

am folosit formulele
1+2+3+4+5+..+n=n*(n+1):2
1+3+5+7+..(2n+1)=(n+1)²