# Math Help - Closed Formula for Geometric Series and Sums

1. ## Closed Formula for Geometric Series and Sums

I just have two questions regarding closed form formulas for geometric series and summing infinite series.

For the closed form formula, I have an expression for the $nth$ term:

$7(7/8)^n$

But I am not sure how to convert this to closed form since I am not really sure what closed form looks like. Is it just to convert it into a finite sum equation like this:

$
\frac{7(1-\frac {7} {8}^n)} {(1- \frac {7} {8})}$

For the infinite series, I have the formula:

$\frac {1} {4} \sqrt{h}$

Where $h = 7(7/8)^n$

So the very first term would be:

$\frac {1} {4} \sqrt{7\frac {7} {8}}$

And this would go in the numerator, but I am not sure what would go in the denominator. I really appreciate everyone's help.

I just have two questions regarding closed form formulas for geometric series and summing infinite series.

For the closed form formula, I have an expression for the $nth$ term:

$7(7/8)^n$

But I am not sure how to convert this to closed form since I am not really sure what closed form looks like. Is it just to convert it into a finite sum equation like this:

$
\frac{7(1-\frac {7} {8}^n)} {(1- \frac {7} {8})}$
This is almost perfect, but remember, the first term of that series is not 7. it is $7 \cdot \frac{7}{8}$.

For the infinite series, I have the formula:

$\frac {1} {4} \sqrt{h}$

Where $h = 7(7/8)^n$

So the very first term would be:

$\frac {1} {4} \sqrt{7\frac {7} {8}}$

And this would go in the numerator, but I am not sure what would go in the denominator. I really appreciate everyone's help.
What's the common ratio? You're taking the square root of $\left(\frac{7}{8}\right)^n$, which is $\left(\frac{7}{8}\right)^{0.5 \cdot n} = \left(\left(\frac{7}{8}\right)^{0.5}\right)^n$.