Suppose if we have a pattern like this $$1=1^3$$ $$3+5=2^3$$ $$7+9+11=3^3$$ and so on.................
I want to know how do I write any $nth$ row in terms of $\sum$ notation?
MY work:
I have figured out that the first term of the each row is of the form $$n^2-n+1$$ and then every row is having a sequence with + 2 with preceding term till n value which can be written as $$\sum_{j=0}^{n-1} n^2 - n+1+2j$$
How to write summation for whole expression? ? Is it possible to write it in single summation ???
Can we write it using double summation also ? Expression the whole equation in summation notation both the sides
The $n$-th row is then $$\sum_{k=0}^{n-1} (n^2-n+1+2k).$$