Sequence And Series Question 416
Question: If the sum to infinity of the series, $ 1+4x+7x^{2}+10x^{3}+…….., $ is 35/16, where $ | x |<1 $ , then x equals to
Options:
A) 19/7
B) 1/5
C) ¼
D) None of these
Show Answer
Answer:
Correct Answer: B
Solution:
[b] $ S=1+4x+7x^{2}+10x^{3}+…….. $ $ x.S=x+4x^{2}+7x^{3}+……. $ Subtract $ S(1-x)=1+3x+3x^{2}+3x^{3}+…… $ $ S(1-x)=1+3x( \frac{1}{1-x} ), $ $ \because ,|x|<1 $ $ S=\frac{1+2x}{{{(1-x)}^{2}}} $ Given: $ \frac{1+2x}{{{(1-x)}^{2}}}=\frac{35}{16} $
$ \Rightarrow ,16+32x=35+35x^{2}-70x,\Rightarrow ,x=\frac{1}{5},\frac{19}{7} $ But $ |x|<1, $
$ \therefore x=1/5 $
BETA
