Show N^M As Sum Of Consecutive N Odd Numbers
(M,N>=2)
Split n^m into n numbers, the average of the numbers would be n^{m-1}.
If n is odd, we can produce the consecutive odd numbers {…n^{m-1}-4, n^{m-1}-2, n^{m-1}, n^{m-1}+2, n^{m-1}+4…}. For example, for 3^3, it will be {7, 9, 11}.
If n is even, we can produce the consecutive odd numbers {…n^{m-1}-5, n^{m-1}-3, n^{m-1}-1, n^{m-1}+1, n^{m-1}+3, n^{m-1}+5…}. For example, for 4^3, it will be {13, 15, 17, 19}.
It can be written as:
Posted by Sha Cheng on Wednesday, December 23, 2020