also
1+x+x^2+x^3........=10
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.)
So:
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.
-Dan