Question

Evaluate:Σ²0 4( 8 )n-1 = [? ]Round to the nearest hundredth.

Answer 1

In this case, we'll have to carry out several steps to find the solution.

Step 01:

Data:

$\sum_{n\mathop{=}1}^{20}4(\frac{8}{9})\placeholder{⬚}^{n-1}$

Step 02:

summa

We must evaluate each term and perform the total sum.

n = 1:

$4\text{ \lparen}\frac{8}{9})\placeholder{⬚}^{1-1}=4(\frac{8}{9})\text{ }^0=4\text{ * 1 = 4 }$

n = 2:

$4\text{ \lparen}\frac{8}{9})\placeholder{⬚}^{2-1}=4(\frac{8}{9})\placeholder{⬚}^1=\text{ 4 * \lparen}\frac{8}{9})=\frac{32}{9}$

The following terms (from 3 to 20) can be evaluated in the same way as above.

total sum:

$\sum_{n\mathop{=}1}^24(\frac{8}{9})\placeholder{⬚}^{n-1}=32.59$

The answer is:

32.59