Cfrgtkky

I am trying to replicate this formula with LaTeX:

However, I am struggling to make the fraction look the same. This is my attempt:

begin{equation}



label{eq:alphaK}



alpha(k) = frac{1}{(N-k)} nicefrac{ left( displaystyle sum_{i=k+1}^{N} lambda_i right) }{left( displaystyle prod_{i=k+1}^N lambda_i right)^{frac{1}{N-k}}}



end{equation}

Which results in the following:

I am looking for a way to increase the size of the "slash" (/) that separates the numerator and denominator. I know I could use a normal frac instead of nicefrac but I like how it looks when num/den are displayed side by side.

Is there any way I can force the fraction to look more like the first pictured one?

There are many ways. You will find two different in some variation below. The last one looks more like your desired output.

documentclass{memoir}

usepackage{amsmath,xfrac,mathtools}



begin{document}

begin{align}

    alpha(k) 

        &=frac{1}{(N-k)} 

            left.

                left(sum_{i=k+1}^{N} lambda_i right)

            right/

            left(prod_{i=k+1}^N lambda_i right)^{sfrac 1{(N-k)}}label{eq:alphaK}\

        &=frac{1}{N-k} 

            left.

                left(sum_{i=k+1}^{N} lambda_i right)

            middle/

                left(prod_{i=k+1}^N lambda_i right)^{frac 1{N-k}}

            right.\

        &=frac{1}{N-k} 

            biggl(,sum_{i=k+1}^{N} lambda_i biggr) 

            bigg/ 

            biggl(,prod_{i=k+1}^N lambda_i biggr)^{1/{(N-k)}}\

            %space added as suggested by Enrico Gregorio

        &=frac

            {sumlimits_{i=k+1}^{N} lambda_i}

            {(N-k), sqrt[N-k]{prodlimits_{i=k+1}^Nlambda_i}} 

        &geq 1 textup{ (by the AM–GM inequality)}

end{align}

end{document}

Remarks.

• Please pay attention to Zarko's comment.




• The nicefrac package might be replaced by https://ctan.org/pkg/xfrac.




• The question mathtools brackets larger than Bigg might be of interest for you.




• Another useful package is https://ctan.org/pkg/mathtools, look for the sections dealing with delimiters.




• Observe that I changed some aspects of the formula, which might collide with your notation.

a small variation of CampanIgnis answer (since he was to fast for my frozen fingers :-( ):

documentclass{article}

usepackage{nccmath}



begin{document}

begin{equation}%label{eq:alphaK}

alpha(k) = frac{1}{(N-k)}

            left(sum_{i=k+1}^{N} lambda_i middle)

            !middle/!

            middle(prod_{i=k+1}^N lambda_i right)^{mfrac{1}{N-k}}

end{equation}

end{document}