Thus, the given sequence becomes,
Which is clearly an H.P.
If G1 and G2 are two geometric means and A is the arithmetic mean inserted between two positive numbers a and b then the value of
Suppose for each n ∈ N.
then an equals
Let A1, A2 be two arithmetic means, G1, G2 be two geometric means, andH1, H2 be two harmonic means between two positive numbers a and b. The value of
Sum of the series
Let x be the arithmetic mean and y, z be the two geometric means between any two positive numbers.