Gas liquid contact in stripping column

[RAfAEL_SP]

$\frac{x[Ain]-x[Aout][/SUB][/SUB]}{x[Ain]-x[out][/SUB][/SUB]}$=$\frac{\sum s^{K}-1}{\sum s^K}$ (1)

for k = 0 to n

Final result:

$\frac{x[Ain]-x[Aout][/SUB][/SUB]}{x[Ain]-x[/SUB][/SUB]}$ = $\frac{{S-S^{n+1}}}{1-S^{n+1}}$

(2)

Does anyone know how to get from (1) to (2).

 

[tiny-tim]

Welcome to PF!

Hi RAfAEL_SP! Welcome to PF!

(use _ not SUB in latex, and use tex rather than itex for fractions that ou don;t want to be too tiny! )

$$\frac{x[Ain]-x[Aout][/SUB][/SUB]}{x[Ain]-x[out][/SUB][/SUB]}$$=$$\frac{\sum s^{K}-1}{\sum s^K}$$ (1)

for k = 0 to n

Final result:

$\frac{x[Ain]-x[Aout][/SUB][/SUB]}{x[Ain]-x[/SUB][/SUB]}$ = $\frac{{S-S^{n+1}}}{1-S^{n+1}}$

(2)

Does anyone know how to get from (1) to (2).

I think you mean $$\frac{\sum s^{K-1}}{\sum s^K}$$
Then eg the denominator is (∑s^K)/(1 - S)

 

[RAfAEL_SP]

The exponent is just k