Question

Demonstrați ca a este pătrat perfect:
a=1+3+5+....+123
a=1+3+5+....+53
a=1+3+5+....+87

Dau coroana

Answer 1

Răspuns:

Explicație pas cu pas:

a=(1+2+3+....+122+123)-2(1+2+3+.......+61)=123×124/2-2×61×62/2=

 =123×62-61×62=62(123-61)=62×62=62²

a=1+2+......+52+53- 2(1+2+.....+26)=53×54/2-2×26×27/2=

  =53×27-26×27=27(53-26)=27²

a=1+2+.....+86+87-2(1+2+...+43)=87×88/2-2×43×44/2=

=87×44-43×44=44(87-43)=44²