SOLUTION: Please put the following polynomial into a simpler form involving a fraction: {{{ 1+x+x^2+x^3+x^4+x^5+x^6+x^7 }}}. I need it to compute the area of the polygon whose vertices are t

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: Please put the following polynomial into a simpler form involving a fraction: {{{ 1+x+x^2+x^3+x^4+x^5+x^6+x^7 }}}. I need it to compute the area of the polygon whose vertices are t      Log On


   



Question 706842: Please put the following polynomial into a simpler form involving a fraction: +1%2Bx%2Bx%5E2%2Bx%5E3%2Bx%5E4%2Bx%5E5%2Bx%5E6%2Bx%5E7+. I need it to compute the area of the polygon whose vertices are the solutions in the complex plane to this same polynomial.
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
+1%2Bx%2Bx%5E2%2Bx%5E3%2Bx%5E4%2Bx%5E5%2Bx%5E6%2Bx%5E7+ is the sum of a geometric sequence.
I always rediscover the formula for a sum, because it's just as easy as looking it up a cumbersome formula and applying it.
S=1%2Bx%2Bx%5E2%2Bx%5E3%2Bx%5E4%2Bx%5E5%2Bx%5E6%2Bx%5E7
Sx=x%2Bx%5E2%2Bx%5E3%2Bx%5E4%2Bx%5E5%2Bx%5E6%2Bx%5E7%2Bx%5E8
Sx-S=x%5E8-1 --> S%28x-1%29=x%5E8-1 --> S=highlight%28%28x%5E8-1%29%2F%28x-1%29%29