Decimals in sigma notation

Question

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

Answer 1

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.