Sequence And Series Question 601
Question: If $ S $ is the sum to infinity of a G.P., whose first term is $ a $ , then the sum of the first $ n $ terms is
[UPSEAT 2002]
Options:
A) $ S{{( 1-\frac{a}{S} )}^{n}} $
B) $ S[ 1-{{( 1-\frac{a}{S} )}^{n}} ] $
C) $ a[ 1-{{( 1-\frac{a}{S} )}^{n}} ] $
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
Let $ r $ be the common ratio of the G.P. Then $ S=\frac{a}{1-r} $
$ \Rightarrow $ $ r=1-\frac{a}{S} $ Now $ S_{n}= $ Sum of $ n $ terms $ =a( \frac{1-r^{n}}{1-r} )=\frac{a}{1-r}(1-r^{n})=S[ 1-{{( 1-\frac{a}{S} )}^{n}} ] $ .
BETA
