Sequence And Series Question 245
Question: If $ a,\ b,\ c $ are in H.P., then the value of $ ( \frac{1}{b}+\frac{1}{c}-\frac{1}{a} ),( \frac{1}{c}+\frac{1}{a}-\frac{1}{b} ) $ , is
[MP PET 1998; Pb. CET 2000]
Options:
A) $ \frac{2}{bc}+\frac{1}{b^{2}} $
B) $ \frac{3}{c^{2}}+\frac{2}{ca} $
C) $ \frac{3}{b^{2}}-\frac{2}{ab} $
D) None of these
Show Answer
Answer:
Correct Answer: C
Solution:
$ a,\ b,\ c $ are in H.P., then $ \frac{1}{a},\ \frac{1}{b},\ \frac{1}{c} $ are in A.P.
$ \Rightarrow $ $ \frac{1}{b}-\frac{1}{a}=\frac{1}{c}-\frac{1}{b} $ Now, $ ( \frac{1}{b}+\frac{1}{c}-\frac{1}{a} ),( \frac{1}{c}+\frac{1}{a}-\frac{1}{b} ) $ $ =( \frac{3}{b}-\frac{2}{a} ),( \frac{1}{b} )=\frac{3}{b^{2}}-\frac{2}{ab} $ .
BETA
