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What would happen if you input a decimal into sigma notation like this: $$\sum_{n=0.5}^2n^2$$ Would this be $0.5^2+1^2+1.5^2+2^2$?

qianqian07
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    The increment by $1$ is not a given fact unless the indexing is being done over natural numbers. However you can specify that in advance and then use the notation by defining your convention. The usual way of expressing this summation on sets with values other than $\mathbb{N}$ is to use $\sum_{a \in {0.5,1,1.5,2}}a^2$. – Anurag A May 12 '20 at 15:23

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Welcome new user. In this form of sigma notation, the running variable, i.e. $n$ is normally supposed to be an integer. If you would like to write your sum $0.5^2+1^2+1.5^2+2$ in sigma notation, you would use $$ \sum_{n=1}^{n=4}\left(\frac{n}{2}\right)^2 $$

Hope this answers your question.

R.J. Etienne
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