Question

Please Help !! Sigma......what is the value of the

Answer 1

Answer:

7

Step-by-step explanation:

Answer 2

You have to count $\sum\limits_{i=1}^{3}\left(4\cdot \left(\dfrac{1}{2}\right)^{i-1}\right)$.
For i=1, 
$4\cdot \left(\dfrac{1}{2}\right)^{i-1}=4\cdot \left(\dfrac{1}{2}\right)^{1-1}=4\cdot \left(\dfrac{1}{2}\right)^{0}=4\cdot 1=4$.
For i=2,
 $4\cdot \left(\dfrac{1}{2}\right)^{i-1}=4\cdot \left(\dfrac{1}{2}\right)^{2-1}=4\cdot \left(\dfrac{1}{2}\right)^{1}=4\cdot\dfrac{1}{2}=2$.
For i=3,
$4\cdot \left(\dfrac{1}{2}\right)^{i-1}=4\cdot \left(\dfrac{1}{2}\right)^{3-1}=4\cdot \left(\dfrac{1}{2}\right)^{2}=4\cdot \dfrac{1}{4}=1$.
Then $\sum\limits_{i=1}^{3}\left(4\cdot \left(\dfrac{1}{2}\right)^{i-1}\right) =4+2+1=7$.
Answer: Correct choice is C.