If H1,H2,....,Hn are n harmonic means between a and b(≠a), then the value of H1+aH1−a+Hn+bHn−b=
A
n+1
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B
n−1
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C
2n
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D
2n+3
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Solution
The correct option is B2n H1H2H3H4... are n harmonic means between a and b.. i.e. 1H11H2... are n arithmetic means between 1a,1b Now we can write, d=1H1−1a d=1b−1Hn Now substitute H1−a and Hn−b in the given expression, we get =1d∗(1b−1a+1Hn−1H1) =(n+1)+(n−1) {since 1b−1a=d(n+1) =2n Hence, option 'C' is correct.