# Is it bad form to omit the variable in a summation equation?

I would like to add variable "a" n times. Usually, a summation has the form $\sum_{k=0}^{n}(a_k)$, $\sum_{k=0}^{n}(a+k)$, etc., but I'm asking about a form $\sum_{k=0}^{n}(a)$. According to Wolfram Alpha, this works fine, but is it a bad practice?

• Yes, you can write that, but what keeps you from writing $a(n+1)$?! – Adrian Nov 23 '16 at 12:18
• @adjan Homework. I just (re)learned summations and products and my instructor wants us to write everything in "proper" notation. I can probably do it simply, but it's hard to read an instructor's mind... – Abluescarab Nov 23 '16 at 12:22
• If you have to sum a n times then the summation starts with k=1 not 0. OR k=0 to n-1 – R_D Nov 23 '16 at 12:27
• @R_D Thanks for the tip. My programmer brain is getting in the way with indices starting at 0. – Abluescarab Nov 23 '16 at 12:28

Sure, you can write $$\sum_{k=1}^n a$$ since this is a perfectly valid mathematical expression. However, since it's equal to $n\cdot a$, I see no reason why you would use the long way to write this.
• @Abluescarab How is $a\cdot n$ not a product? – Adrian Nov 23 '16 at 12:24
• @adjan I meant the "product" with the $\prod_{k=0}^{n}$ form. – Abluescarab Nov 23 '16 at 12:26
We have $\sum_{k=0}^{n}a=(n+1)a$. Reason:
Put $b_k:=a$ for $k=0,1,...,n$ and consider $\sum_{k=0}^{n}b_k$