Is there a notation for summing a non-variable set of exponents

Question

Given a static (not variable) range of integers, such as One Through Five, I have this equation.

$b^1$ + $b^2$ + $b^3$ + $b^4$ + $b^5$

Is there a shorter way to write that, knowing that this is not a variable set of exponents, but only with this static range?

Also, without using Sigma if possible, as I can see where n is from 1 to 5, but trying to avoid that.

Also, without using functions f(), if possible.

I'm imagining something, though this is probably wrong, like $3^{5!}$, or $3^{1 to 5}$ though that notation doesn't really exist I believe.

Why do you want to avoid $\sum$? The standard notation for what you want is $\sum_{j=1}^5b^j$. — David C. Ullrich, May 19 '20 at 19:04
you can use any notation you want as long as you indicate what it means — Donlans Donlans, May 19 '20 at 19:06
I forgot about ellipses to represent "obvious pattern". I do like that as an option. Given some time, if that is the only best answer, it is reasonable, and I would select it if there were no other answers. — Suamere, May 19 '20 at 19:26

score 1 · Accepted Answer · edited May 19 '20 at 19:59

If it's clear from context what the exponents vary over, then you can write $b^1 + \dots + b^5,$ although usually one would write this as $b^1 + b^2 + \dots + b^5.$ However, if you're only going from $1$ to $5$ (or ranging over even fewer many integers), then it doesn't seem worth writing anything more abbreviated than $b^ 1 + b^2 + b^3 + b^4 + b^5.$ The two versions I gave using "$\dots$" are more useful when the integers range over a larger set.

For examples, see the use of "$\dots$" at Sum of the form $r+r^2+r^4+\dots+r^{2^k} = \sum_{i=1}^k r^{2^i}$, which I happened to think of because I recently cited this in a Mathematics Stack Exchange comment for another question.

Is there a notation for summing a non-variable set of exponents

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