The series 632334 converges to the sum a 24 b 32 c 12 d 18 e

The series 6+3+(2/3)+(3/4)+... converges to the sum:

a. 24 b. 32 c. 12. d. 18 e. 57

Solution

the series should be 6+3+(3/2)+(3/4)+...

then only it is perfectly in geometric progression with a = 6 and r = 0.5

now as 0< r < 1. it will be converging and sum is given by

sum = a/(1-r)

= 6/(1-0.5)

= 6/0.5

= 12 (option C)