Questions
If are harmonic means between and , then value of is equal to
detailed solution
Correct option is C
As a,H1,H2,…,Hnb are in H.P. 1a,1H1,1H2⋯1Hn,1b are in A.P.Let dbe the common difference of this A.P., then 1b=1a+(n+1)dand 1Hn−1H1=(n−1)dNow, H1+aH1−a=1/a+1/H11/a−1/H1=1/a+1/H1−dand Hn+bHn−b=1/b+1/Hn1/b−1/Hn=1/b+1/Hnd∴ H1+aH1−a+Hn+bHn−b=1/a+1/H1−d+1/b+1/Hnd =1d1b−1a+1Hn−1H1=2nSimilar Questions
Two possible observations have arithmetic mean 3 and geometric mean .If each observation is multiplied by 2, then harmonic mean will be
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