3 years ago

Solve y = mx + b for x

Mathematics

1 answer:

eimsori [14]3 years ago

8 0

Y=mx+b
-b -b
--------------
-by= mx
-------------
m m

-by
------
m

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$\dfrac1{z(z-2)} = \dfrac12 \left(\dfrac1{z-2} - \dfrac1z\right)$

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Then for |z| > 2, or |1/(z/2)| = |2/z| < 1, we have

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So the series expansion of f(z) for |z| > 2 is

$\displaystyle f(z) = \frac12 \left(\sum_{n=0}^\infty \frac{2^n}{z^{n+1}} - \frac1z\right)$

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$\displaystyle f(z) = \sum_{n=1}^\infty \frac{2^{n-1}}{z^{n+1}}$

$\displaystyle \boxed{f(z) = \frac14 \sum_{n=2}^\infty \frac{2^n}{z^n} = \frac1{z^2} + \frac2{z^3} + \frac4{z^4} + \cdots}$

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