Sequence And Series Question 611
Question: $ 1+\frac{3}{2}+\frac{5}{2^{2}}+\frac{7}{2^{3}}+……,\infty , $ is equal to
[DCE 1999]
Options:
A) 3
B) 6
C) 9
D) 12
Show Answer
Answer:
Correct Answer: D
Solution:
It is an arithmetico-geometric series $ {S_{\infty }}=\frac{a}{1-r}+\frac{dr}{{{(1-r)}^{2}}} $ $ =\frac{1}{1-\frac{1}{2}}+\frac{2}{{{( 1-\frac{1}{2} )}^{2}}} $ $ =\frac{2}{\frac{1}{2}}+\frac{2}{\frac{1}{4}} $ $ =4+8=12 $ .
BETA
