Question

Find the sum of the geometric series.
5
Σ 2(-4)k
k=1

Answer 1

is that (-4)^k or (-4)*k

Answer 2

since its geometric, ill assume k is the exponent
2 is a constant so it can be pulled out of sum
formula for sum of geometric sequence is
\[s _{n}=\frac{a _{1}(1-r ^{n})}{1-r}\]
r = -4, n =5, a=-4
s = -4(1-(-4)^5)/(1-(-4))
s = -4(1+1024)/5
s = -820

Answer 3

oops
then multiply by 2
s = -820*2
s=-1640

Answer 4

but wait a min, since it's a geometric series, you'lk have to take the absolute value of r , |r| = |-4| = 4 >1, in this case, since R > 1 then the following series is said to diverge, right? .-.