we are given
[tex] \sum _{i=1}^3\:\left(4\cdot \left(\frac{1}{2}\right)^{i-1}\right) [/tex]
now, we can expand it
[tex] \sum _{i=1}^3\:\left(4\cdot \left(\frac{1}{2}\right)^{i-1}\right)=(4*(\frac{1}{2} )^{1-1})+(4*(\frac{1}{2} )^{2-1})+(4*(\frac{1}{2} )^{3-1}) [/tex]
now, we can simplify it
we get
[tex] \sum _{i=1}^3\:\left(4\cdot \left(\frac{1}{2}\right)^{i-1}\right)=7 [/tex]
option-D.......Answer
