For this case, we must expand the series for each value of "n". That is to say:[tex]2 ^ {(1) -2} +2 ^ {(2) -2} +2 ^ {(3) -2} +2 ^ {(4) -2} +2 ^ {(5) -2} =[/tex]
We have that equal signs are added and the same sign is placed, while different signs are subtracted and the sign of the major is placed:
2 ^ {1-2} + 2 ^ {2-2} + 2 ^ {3-2} + 2 ^ {4-2} + 2 ^ {5-2} =
[tex]2 ^ {-1} + 2^{0}+ 2^{1} + 2^{2} + 2^{3}=[/tex]
By definition of power properties we have to:
[tex]a ^ {-1} = \frac {1} {a}\\a ^ 0 = 1[/tex]
So:
[tex]\frac {1} {2} + 1 + 2 + 4 + 8 =[/tex]
We find the common denominator:
[tex]\frac {1} {2} + 1 * \frac {2} {2} + 2 * \frac {2} {2} + 4 * \frac {2} {2} + 8 * \frac {2} { 2} =\\\frac {1 + 2 + 4 + 8 + 16} {2} =\\\frac {31} {2} =\\15.5[/tex]
Answer:
Option B
