# How do we treat continuous variables inside summations?

I've been getting confused everytime we're graphing a summation with a continuous variable inside. For example, say I want to graph this equation with respect to $$f$$ ($$y$$ vertical, $$f$$ horizontal)

$$y = 5\sum_{k=0}^\infty \operatorname{sinc}^2 \left(\frac k2 \right) \delta(f-k)$$

How do I account for the continuous variabality of $$f$$ inside? I know this maps to a comb function multiplied by varying constants, but I don't get how f is dealt with. Doesn't it vary continously with $$k$$?

• Welcome to Math SE! When you have a minute, please take the tour of the site and look at how to format mathematics here on Math SE. Also, I suggest that you bookmark this very useful MathJax page for quick reference. Cheers! – Vee Hua Zhi Nov 9 '18 at 12:11
• I suggest you type out the equation (using MathJax, if possible) and only include pictures only if it is absolutely necessary. – Vee Hua Zhi Nov 9 '18 at 12:16
• @Tralala Done. I hope this makes things clearer. – M Zein Nov 9 '18 at 12:29
• Hmm, your summation variable $i$ is not mentioned at all in the expression you're summing over ... should it have been $k$? – hmakholm left over Monica Nov 9 '18 at 12:34
• @HenningMakholm Oh sorry, yes it should have been k. Wrote I by mistake because it was in the MathJax tutorial. – M Zein Nov 9 '18 at 12:37