Is There a Difference Between These Two Notations for Infinite Summation?

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The discussion clarifies that there is no substantive difference between the notations \lim_{n\rightarrow\infty}\sum_{i=1}^{n} and \sum_{n=1}^{\infty}, as both represent the same concept of infinite summation. The distinction lies solely in their presentation, with one requiring less notation than the other. Participants humorously note the practicality of conserving ink in academic settings. Overall, the conversation emphasizes the equivalence of the two expressions in mathematical terms. The lighthearted tone highlights the simplicity of the notation debate.
Icebreaker
Is there a difference between \lim_{n\rightarrow\infty}\sum_{i=1}^{n} and \sum_{n=1}^{\infty}?
 
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Nevermind. The latter is defined as the former.
 
Yes,that means that the difference is only in writing...One required less ink (or LaTex code) than the other...:-p

Daniel.
 
Ya, the math departments are so strapped for cash they must conserve ink. :smile:
 

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