Hello,
I have an expression of radicals which I know simplify to the closed form
expression for the fibonacci sequence, but I cannot make it appear as nice
as I know it should be:
matrix([-((sqrt(5)-1)^t*2^(-t-1)*(-1)^t)/sqrt(5)+(sqrt(5)-1)^t*2^(-t-1)*(-1)^t+((sqrt(5)+1)^t*2^(-t-1))/sqrt(5)+(sqrt(5)+1)^t*2^(-t-1)],[(sqrt(5)+1)^t/(sqrt(5)*2^t)-((sqrt(5)-1)^t*(-1)^t)/(sqrt(5)*2^t)])
But I cannot seem to find the correct function to reduce this to:
matrix([
[( ((1+sqrt(5))/2)^(t+1) - ((1-sqrt(5))/2)^(t+1)) / sqrt(5)],
[( ((1+sqrt(5))/2)^t - ((1-sqrt(5))/2)^t ) / sqrt(5)
])
I've tried the standard things such as radcan, fullratsimp, algebraic:
true, but I cannot get it to simplify.