Question

Sum of ${}^{\prime }{n}^{\prime }$ odd number of consecutive numbers is divisible by ${}^{\prime }{n}^{\prime }$. Explain the reason

Answer 1

Sum of $n$ consecutive odd numbers (Like $1,3,5,\mathrm{7..........}n$) =$n^2$
And , we can see that $n^2$ is always be divisible by $n$.
Therefore, Sum of $n$ odd consecutive numbers will be always divisible by $n$.