Statistics - help Prophet Sir

1. If 2u=5x and the harmonic mean of x is 0.4, What is the harmonic mean of u?

2.Statistics Sum If a variable 'x' takes the values 1,2,3,.....,k with F₁,F_2,,..... F_k as the corresponding more than type cumulative frequencies, then prove that
\bar{x} = \frac{1}{N} \sum_{i=1}^{k}{F_{i}} where N = F_{i} is the total frequency.

3. If two sets of Positive values in which there are n₁ and n₂ variables and the geometric means of which are G₁ and G₂ respectively and G be their combined mean, then show that
G₁ < G < G₂

I'm not sure of equality sign there!

4. Find the weighted HM of first n natural numbers with weight proportional to the corresponding value.