Write $(1^3 −1)−(2^3 −1)+(3^3 −1)−(4^3 −1)+(5^3 −1)$ using summation or product notation.

Question

Question: Write the following using summation or product notation:

$$(1^3 −1)−(2^3 −1)+(3^3 −1)−(4^3 −1)+(5^3 −1)$$

I have got following conversion, however it looks a bit over complicated:

$$\sum_{j=1}^5 (-1) ^ {j-1} (j^3-1) $$

Can you please suggest a simpler, better one?

Answer 1

It doesn't look that complicated. I don't think you can make it much better, and $\prod$ notation certainly wouldn't work here.