If is root of equation then find the value of

Here I have put the value of in the given equation to get which is similar to the first three terms. So, each three terms give value = 0 . Only the last term will remain which is

Can we equate this with the help of Geometric progression somehow....as the given terms form a G.P with first term 1 and common ratio

Sum of the n terms of G.P = where r is common ratio .

Please suggest.