Sequence And Series Question 22
Question: If $ \frac{{a^{n+1}}+{b^{n+1}}}{a^{n}+b^{n}} $ be the harmonic mean between $ a $ and $ b $ , then the value of $ n $ is
[Assam PET 1986]
Options:
A) 1
B) $ -1 $
C) 0
D) 2
Show Answer
Answer:
Correct Answer: B
Solution:
We have $ \frac{{a^{n+1}}+{b^{n+1}}}{a^{n}+b^{n}}=\frac{2ab}{a+b} $
$ \Rightarrow $ $ {a^{n+2}}+a{b^{n+1}}+b{a^{n+1}}+{b^{n+2}}=2{a^{n+1}}b+2{b^{n+1}}a $
$ \Rightarrow $ $ {a^{n+1}}(a-b)={b^{n+1}}(a-b) $ or $ {{( \frac{a}{b} )}^{n+1}}=(1)={{( \frac{a}{b} )}^{0}} $ Hence $ n=-1 $ .
BETA
