Hello,
\(\sum_{i=0}^{k-1}\ (2*i+1)=2*\sum_{i=0}^{k-1}\ i +\sum_{i=0}^{k-1}\ 1\\
= \dfrac{k*(k-1)}{2} +k=k^2-k+k=k^2\)
In details:
s= 1 +3 +5+7+9+.... +2(k-2)+1 +2(k-1)+1
s= 2(k-1)+1 +2(k-2)+1 +.... +9+7+5 +3 +1
2s=(2k-2+2) +(2k-4+4)+...........................................+(2k-2+2)
=2k+2k+2k+....+2k (there is k terms)
2s=2k*k
2s=2k²
s=k²
Answer J
