There must be a simpler way

Algebra Level 4

Let ${ a }_{ 1 }, { a }_{ 2 }, { a }_{ 3 }, \ldots ,{ a }_{ 17 }$ be the roots of the equation ${ x }^{ 17 }+17x-2015=0$ . Find the value of the sum below.

$\large { { a }_{ 1 } }^{ 17 }+{ { a }_{ 2 } }^{ 17 }+{ { a }_{ 3 } }^{ 17 }+\cdots +{ { a }_{ 16 } }^{ 17 }+{ { a }_{ 17 } }^{ 17 }$

The answer is 34255.

1 solution

Deepak Kumar
Jan 13, 2016

Hint:Write x^17=2015-17x and use the fact that sum of roots of given polynomial=0 as there is no term ccontaining x^16!!

There must be a simpler way

The answer is 34255.

1 solution

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