How do you convert this summation to dot notation?

[Atria]

[math]\sum_{\ell=1}^{u-1} b_{u+1}[/math]

 

[Harry_the_cat]

For this to make sense, there should be an [imath]\ell[/imath] in the expression after the sigma sign.

 

[Atria]

For this to make sense, there should be an [imath]\ell[/imath] in the expression after the sigma sign.

so you are saying that it is totally incorrect notation?

 

[Dr.Peterson]

so you are saying that it is totally incorrect notation?

It isn't totally incorrect, but it surely doesn't mean what you intend! The value of the sum is just [imath](u-1)b_{u+1}[/imath], because you are adding up [imath]u-1[/imath] copies of the constant [imath]b_{u+1}[/imath].

There's also the question of what "dot notation" means! Perhaps you mean expanding the summation into an explicit sum, which as written would be [imath]\underset{u-1}{\underbrace{b_{u+1}+b_{u+1}+\dots+b_{u+1}}}[/imath].