Question

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

Answer 1

7

Explanation:

Answer 2

You have to count
`\sum\limits_(i=1)^(3)\left(4\cdot \left((1)/(2)\right)^(i-1)\right)`.
For i=1,

`4\cdot \left((1)/(2)\right)^(i-1)=4\cdot \left((1)/(2)\right)^(1-1)=4\cdot \left((1)/(2)\right)^(0)=4\cdot 1=4`.
For i=2,

`4\cdot \left((1)/(2)\right)^(i-1)=4\cdot \left((1)/(2)\right)^(2-1)=4\cdot \left((1)/(2)\right)^(1)=4\cdot(1)/(2)=2`.
For i=3,

`4\cdot \left((1)/(2)\right)^(i-1)=4\cdot \left((1)/(2)\right)^(3-1)=4\cdot \left((1)/(2)\right)^(2)=4\cdot (1)/(4)=1`.
Then
`\sum\limits_(i=1)^(3)\left(4\cdot \left((1)/(2)\right)^(i-1)\right) =4+2+1=7`.
Answer: Correct choice is C.