Thread: Geometric Series....got it down to algebra...but i can figure it out

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)

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

Originally Posted by stones44

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

Originally Posted by stones44

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

This one, ironically, we can solve.



So










-Dan

arent you supposed to do last *multipler - first / multipler - 1

and the multipler is X and first is x because 1 is like a seperate thing (not part of the series)

Originally Posted by stones44

arent you supposed to do last *multipler - first / multipler - 1

and the multipler is X and first is x because 1 is like a seperate thing (not part of the series)

Here you have


So a = 1, the coefficient of in the sum, otherwise known as the first term in the summation, and r = x, the geometric ratio.

What you tried to do was this:




There is nothing wrong in doing this, but now your series is

so a = x and r = x.

-Dan