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Question

If H1,H2,....,Hn are n harmonic means between a and b(a), then the value of H1+aH1a+Hn+bHnb=

A
n+1
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B
n1
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C
2n
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D
2n+3
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Solution

The correct option is B 2n
H1H2H3H4... are n harmonic means between a and b..
i.e. 1H11H2... are n arithmetic means between 1a,1b
Now we can write,
d=1H11a
d=1b1Hn
Now substitute H1a and Hnb in the given expression, we get
=1d(1b1a+1Hn1H1)
=(n+1)+(n1) {since 1b1a=d(n+1)
=2n
Hence, option 'C' is correct.

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