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((8)/(9))\placeholder{⬚}^(n-1)`

Step 02:

summa

We must evaluate each term and perform the total sum.

n = 1:

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

n = 2:

`4\text{ \lparen}(8)/(9))\placeholder{⬚}^(2-1)=4((8)/(9))\placeholder{⬚}^1=\text{ 4 * \lparen}(8)/(9))=(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((8)/(9))\placeholder{⬚}^(n-1)=32.59`

The answer is:

32.59