Finding sum of infinite series.

Question

finding the sum of the following infinite series

 

a) 2,-4,8,-16,...

b)3,9,27,81,...

c)60,30,15,...

 

Final exam coming up and I'm stressing thanks so much

Answer 1

A geometric series has a finite sum a₁/(1-r) when the common ratio, r, satisfies the inequality -1 < r < 1.  Otherwise, the series diverges.  

 

So, for the geometric series in part (a), r = -2.  Consequently, the

series is divergent.  For the geometric series in part (b), r = 3. Therefore, the series diverges.  In part (c), the series is geometric with r = 1/2.  Since r is between -1 and 1, the series converges and has sum 60/(1-(1/2)) = 120.      

Answer 2

For a geometric series:

 

S = a₁ / (1 - r)

 

For a)

 

S = 2 / (1 - (-2))

S = 2 / 3

 

For b) and c) substitute the appropriate first term and common ratio.