Question

What is the sum of this geometric series?(picture of problem below)

Answer 1

`D)(21)/(2)`

1) Since this is a series, a geometric we can expand this, note that the common ratio is in the parentheses.

`\begin{gathered} \sum_(n=1)^38\cdot\left((1)/(4)\right)^(k-1)=8\cdot\left((1)/(4)\right)^(1-1)+8\cdot\left((1)/(4)\right)^(2-1)+8\cdot\left((1)/(4)\right)^(3-1) \\ \\ \placeholder{⬚}^1 \\ \end{gathered}`

Note We plugged into k the number of the term from 1 to 3.

2) So we can solve it this way:

`8\cdot((1)/(4))^0+8\cdot((1)/(4))^1+8\cdot((1)/(4))^2=(21)/(2)`

Thus the answer is 21/2