Solving an equation of sums

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Konstantinos
Konstantinos 2015-2-2
评论： Konstantinos 2015-2-3
I want to find y in an equation which has the following form:
1/(1+y)^1 + 1/(1+y)^2 + 1/(1+y)^3 + 1/(1+y)^4 + 1/(1+y)^5 + 1/(1+y)^6 + 1/(1+y)^7 = c
where c is a known constant real value.
Any help could be useful. thanks in advance!

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Torsten
Torsten 2015-2-2
Use "roots" to calculate the real zero x0 of the polynomial
p(x)=x^8-(1+c)*x+c.
Then y0=1/x0-1 will solve your above equation.
Best wishes
Torsten.
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Torsten
Torsten 2015-2-2
Geometric series:
x+x^2+x^3+x^4+x^5+x^6+x^7=(x^8-1)/(x-1) - 1 = (x^8-x)/(x-1)
with x=1/(1+y)
Best wishes
Torsten.

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