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# Z-transforms - summation of an infinite series watch

1. How would i some the infinite series 2z + 6z^2 + 12z^3 + 20z^4 + .....? The first term is obviously 2z but what is the common ratio? I see that it will include z but I don't know how to sum for the co-efficents.
2. 2z(1 + 3z^2 + 4z^3 + 5z^4 + ...

= 2z( -2z + 1 + 2z + 3z^2 + 4z^3 + ...

=2z(-2z + [(d/dz)(z + z^2 + z^^3 + z^4 + ...])
3. Dean: the series you have summed is not the series the OP has posted.

Differentiating (z+z^2+z^3+...) twice should be fruitful.

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Updated: February 4, 2010
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