Equation opening

[Batzo]

Hi everyone,
My first time here so thank you

I want to know how to open equation of c for more than i=2.

 

[Deleted member 4993]

Hi everyone,
My first time here so thank you

I want to know how to open equation of c for more than i=2.

View attachment 28338

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[Eugenio]

For $i=2$ you have $M(M^{-1}K)^2=MM^{-1}KM^{-1}K=IKM^{-1}K=KM^{-1}K$

For $i=3$ you have $M(M^{-1}K)^3=MM^{-1}KM^{-1}KM^{-1}K=IKM^{-1}KM^{-1}K=K(M^{-1}K)^2$

For $i=4$ you have $M(M^{-1}K)^4=K(M^{-1}K)^3$

And for $i=n$ you have $M(M^{-1}K)^n=K(M^{-1}K)^{n-1}$