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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?

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    $\begingroup$ Yes, you can write that, but what keeps you from writing $a(n+1)$?! $\endgroup$ – Adrian Nov 23 '16 at 12:18
  • $\begingroup$ @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... $\endgroup$ – Abluescarab Nov 23 '16 at 12:22
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    $\begingroup$ If you have to sum a n times then the summation starts with k=1 not 0. OR k=0 to n-1 $\endgroup$ – R_D Nov 23 '16 at 12:27
  • $\begingroup$ @R_D Thanks for the tip. My programmer brain is getting in the way with indices starting at 0. $\endgroup$ – Abluescarab Nov 23 '16 at 12:28
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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.

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  • $\begingroup$ Thanks. I considered this, of course, but this pertains to a homework assignment where we have to write things out in terms of summations and products, and it's difficult to know exactly what an instructor wants! $\endgroup$ – Abluescarab Nov 23 '16 at 12:23
  • $\begingroup$ @Abluescarab How is $a\cdot n$ not a product? $\endgroup$ – Adrian Nov 23 '16 at 12:24
  • $\begingroup$ @adjan I meant the "product" with the $\prod_{k=0}^{n}$ form. $\endgroup$ – Abluescarab Nov 23 '16 at 12:26
  • $\begingroup$ @Abluescarab ok, gotcha. $\endgroup$ – Adrian Nov 23 '16 at 12:28
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We have $\sum_{k=0}^{n}a=(n+1)a$. Reason:

Put $b_k:=a$ for $k=0,1,...,n$ and consider $\sum_{k=0}^{n}b_k$

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