# Bashing unavailable - part 5

Algebra Level 4

Given that

$\color{#20A900}{a+b+c =1}$

$\color{#3D99F6}{a^2+b^2+c^2=2}$

$\color{#D61F06}{a^3+b^3+c^3=3}$

Then $a^4+b^4+c^4= \frac{a_1}{a_2}$ .... where $a_1$ and $a_2$ are positive coprime integers.

And $a^5+b^5+c^5=a_3$ ...... where $a_3$ is an integer.

And $a^6+b^6+c^6= \frac{a_4}{a_5}$ ....where $a_4$ and $a_5$ are positive coprime integers.

And $a^7 +b^7+c^7= \frac{a_6}{a_7}$ ....where $a_6$ and $a_7$ are positive coprime integers.

And $a^8+b^8+c^8 = \frac{a_8}{a_9}$ ... where $a_8$ and $a_9$ are positive coprime integers.

Find $a_1+a_2+a_3+a_4+a_5+a_6+a_7+a_8 +a_9$.

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