Question

what is the formula for sum of n harmonic mean.

Answer 1

Answer:

H = 2ab/a+b

Let us assume that Ha and Hb are two harmonic means between a and b. Then it follows that a, Ha, Hb and b are in H.P. Then 1/a, 1/Ha, 1/Hb, 1/b are in A.P. Hence, using the formula we have. tn = a + (n-1)d.

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Answer 2

❤1b=(n+2)th term=Tn+2. 1b=1a+(n+1)D ⇒ D=a-b(n+1)ab. Thus, if n harmonic means are inserted between two given numbers a and b, then the common difference of the corresponding A.P. is given by D=a-b(n+1)ab. Also, 1H1=1a+D, 1H2=1a+2D,.......,1Hn=1a+nD, where D=a-b(n+1)ab.❤

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