Answer:
Sum is -3577/256
Step-by-step explanation:
This is a geometric progression:
[tex]S = \frac{a( 1 - {r}^{n} )}{1 - r } \\ for \: \: r < 1[/tex]
S is the sum
a is the first term, a = -7
r is the common ratio, r = -7/2 ÷ -7 = ½
substitute:
[tex]S = \frac{ - 7(1 - {( \frac{1}{2}) }^{9} }{1 - \frac{1}{2} } \\ \\ S = \frac{ - 6.986}{ \frac{1}{2} } \\ \\ S = - \frac{3577}{256} [/tex]
