Proof This can be proved by mathematical induction.
Proof
This can be proved by mathematical induction.
Assume it is true for n=k, then
1+3+5+...+(2k-1)=k2
add the next item (2k+1).
Then 1+3+5+...+(2k-1)+(2k+1)=k2+(2k+1)=(k+1)2.
Therefore if it is true for n=k it is true for n=k+1.
It is true for n=1 therefore it is true for all values of n.