Find the sum to infinity of the series 1/2 , 1/6, 1/18, …..
-
A.
2/3 -
B.
1/3 -
C.
3/4 -
D.
1
Correct Answer: Option C
Explanation
(a=frac{1}{2}\r=frac{frac{1}{6}}{frac{1}{2}}=frac{1}{6}timesfrac{2}{1}=frac{1}{3}\S_infty = frac{a}{1-r}\S_infty = frac{frac{1}{2}}{1-frac{1}{3}}\=frac{frac{1}{2}}{frac{3}{2}}\=frac{1}{2}timesfrac{3}{2}\=frac{3}{4})