set it up: (0-x)/(x-1) = 9 so x = .9
but i did it using my calc also
im clearly missing a big piece of algebra knowledge
so it was
If 1+x+x^2+x^3+.....+x^24=10 what is x
so i got
((x^25) - x) / (x -1) = 9
and i put in my calc and got the right answer..but how can i do it just by solving the algebra?
the answer is .90927693 (almost positive)
(Note the difference between my formula and yours. I took a0 = 1 and n = 24. You took a0 = x and n = 24. Clearly your n should have been 23.)
You want to find an exact root of this equation? Can't be done in general. There are no rational roots, at least, so we are stuck with numerical approximation.