How to solve this double summation with a variable stopping point?

72 Views Asked by At

I know how to solve basic double summations but, i have trouble with this one, specifically I don't know how to begin since the end point of the inner summation is not an independent value. $$ \Sigma^4_{i=1}\Sigma^i_{j=1} (ij-1)\, $$

1

There are 1 best solutions below

2
On BEST ANSWER

It's $$\sum_{j=1}^11(j-1)+\sum_{j=1}^2(2j-1)+\sum_{j=1}^3(3j-1)+\sum_{j=1}^4(4j-1)=$$ $$=1+2(1+2)+3(1+2+3)+4(1+2+3+4)-1-2-3-4=55$$