A few days ago, EcoDTR posted a question about a number series to which Soroban made a reply including this statement:
Can you elaborate a little bit on how to solve for x in the case of a finite power series? I.E. 1 + x + x^2 + x^3 + ... + x^24 + x^25 + x^26 = y?If the problem was actrually: 1 + x + x^2 + x^3 + ... = 5
. . we can solve for x . . . otherwise, forget it!
For y=244, I know the answer is approximately 1.1413211694 through trial and error using my computer to run out the summation as I plugged in numbers. Now I'd like to know the math behind why that is the answer or how I can calculate x given a known y. Any pointers?