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## Homework Statement

Find the sum of the series

[itex]\displaystyle S_1=1 + \frac{x^3}{3!}+\frac{x^6}{6!}+\,\dots[/itex]

Can't seem to get the bit above to show up nicely, should be 1+x^3/3! +x^6/6! +... Sorry!!

## Homework Equations

In a prior part of the question I had to find the complex roots of z

^{3}-1=0 which I did and got:

1, e

^{[itex]\frac{2\pi}{3}[/itex]}, e

^{[itex]\frac{4\pi}{3}[/itex]}

and then by writing z

^{3}-1=0 as being equal to the product of its roots I was able to show that [itex]\omega[/itex]

^{2}+[itex]\omega[/itex]+1=0 where [itex]\omega[/itex] is a complex root

## The Attempt at a Solution

Using all of this I then have to solve the summation so I'm sure that the prior questions have something to do with solving the summations I'm just not really sure how to relate them. I've only really been able to look at maclaurin series' for various functions but have had no joy as to further inspiration.

Any help would be greatly appreciated, thank you in advance!

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