- #1
LCSphysicist
- 646
- 161
- Homework Statement
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- Relevant Equations
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if x_{I}, I = {1,2,...,2019} is a root of P(x) = ##x^{2019} +2019x - 1##
Find the value of ##\sum_{1}^{2019}\frac{1}{1-\frac{1}{X_{I}}}##
I am really confused:
This polynomial jut have one root, and this root is x such that 0 < x < 1, so that each terms in the polynomial is negative. But the alternatives just give positive values.
This makes me think we need to consider the complex root of this. But i have no idea how to find them.
Maybe calling ##x = re^{i\theta}## give us:
##0 = r^{2019}e^{i2019\theta}+ 2019re^{i\theta} - 1##
?
Find the value of ##\sum_{1}^{2019}\frac{1}{1-\frac{1}{X_{I}}}##
I am really confused:
This polynomial jut have one root, and this root is x such that 0 < x < 1, so that each terms in the polynomial is negative. But the alternatives just give positive values.
This makes me think we need to consider the complex root of this. But i have no idea how to find them.
Maybe calling ##x = re^{i\theta}## give us:
##0 = r^{2019}e^{i2019\theta}+ 2019re^{i\theta} - 1##
?