Evaluate each infinite geometric series described

Question

13) a1 = 3, r = −1/5

14) a1 = 1, r = −4

15) a1 = 1, r = −3

16) a1 = 1, r = 1/2

Answer 1

13)

Given a  =  3 and r  =  -1/5

The sum of the infinite series in GP is

S = a / (1 - r)

Substitute a  =  3 and r  =  -1/5 in above equation

S = 3 / (1 + 1/5)

S = 3 / [(5 + 1)/5]

S = 3 / [(6/5]

S = (3 X 5) / 6

S = 5/2

S  =  2.5

 

14)

Given a  =  1 and r  =  -4

The sum of the infinite series in GP is

S = a / (1 - r)

Substitute a  =  1 and r  =  - 4 in above equation

S = 1 / (1 + 4)

S = 1/5

S  =  0.2

 

15)

Given a  =  1 and r  =  -3

The sum of the infinite series in GP is

S = a / (1 - r)

Substitute a  =  1 and r  =  - 3 in above equation

S = 1 / (1 + 3)

S = 1/4

S  =  0.25

 

16)

Given a  =  1 and r  =  1/2

The sum of the infinite series in GP is

S = a / (1 - r)

Substitute a  =  1 and r  =  1/2 in above equation

S = 1 / (1 - 1/2)

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

S = 1/(1/2)

S  =  2