# indefinite sum definition

**URL:** <https://community.wolfram.com/t/indefinite-sum-definition/11480>\
**Category:** Questions\
**Tags:** algebra, calculus\
**Created:** [November 6, 2017, 1:20pm UTC](https://community.wolfram.com/t/indefinite-sum-definition/11480 "2017-11-06T13:20:05Z")\
**Posts on this page:** 2\
**Page:** 1

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**Author:** ![luqingchina](https://avatars.discourse-cdn.com/v4/letter/l/8c91f0/32.png) [@luqingchina](https://community.wolfram.com/u/luqingchina)\
**Post date:** [November 6, 2017, 1:20pm UTC](https://community.wolfram.com/t/indefinite-sum-definition/11480/1 "2017-11-06T13:20:05Z")

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Hello, I am new to the Mathematica, so please tolerate with my naive question. Here I have a question about the indefinite summation, e.g.

input: Sum[i^3, i]  
Output: 1/4(-1+i)^2\*i^2

If I let i ranges from 1 to 1, e.g. {i,1,1}, the summation is 1. But according to the output expression, the result is 0. Why is that?

Thank you.

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<div class="post-metadata">

**Author:** ![gianlucagorni](https://avatars.discourse-cdn.com/v4/letter/g/ec9cab/32.png) [@gianlucagorni](https://community.wolfram.com/u/gianlucagorni)\
**Post date:** [November 6, 2017, 2:53pm UTC](https://community.wolfram.com/t/indefinite-sum-definition/11480/2 "2017-11-06T14:53:29Z")

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Your input `Sum[i^3, i]` is similar to an indefinite integral, which is defined only up to an additive constant. The output is correct in the following sense:

```
In[538]:= a[i_] = Sum[i^3, i];
a[i + 1] - a[i] // Simplify

Out[539]= i^3

```