Let $$\mathrm{A_{1}, G_{1}}, \mathrm{H}_{1}$$ denote the arithmetic, geometric and harmonic means, respectively, of two distinct positive numbers. For $$n \geq 2$$, let $$\mathrm{A}_{n-1}$$ and $$\mathrm{H}_{n-1}$$ have arithmetic, geometric and harmonic means as $$\mathrm{A_{n}}$$, $$\mathrm{G}_{\mathrm{n}}, \mathrm{H}_{\mathrm{n}}$$ respectively.

Which one of the following statements is correct?

Let $$\mathrm{A_{1}, G_{1}}, \mathrm{H}_{1}$$ denote the arithmetic, geometric and harmonic means, respectively, of two distinct positive numbers. For $$n \geq 2$$, let $$\mathrm{A}_{n-1}$$ and $$\mathrm{H}_{n-1}$$ have arithmetic, geometric and harmonic means as $$\mathrm{A_{n}}$$, $$\mathrm{G}_{\mathrm{n}}, \mathrm{H}_{\mathrm{n}}$$ respectively.

Which one of the following statements is correct?

Let V$$_r$$ denote the sum of the first r terms of an arithmetic progression (A.P.) whose first term is r and the common difference is ($$2r-1$$). Let $${T_r} = {V_{r + 1}} - {V_r} - 2$$ and $${Q_r} = {T_{r + 1}} - {T_r}$$ for r = 1, 2, ...

The sum V$$_1$$ + V$$_2$$ + ... + V$$_n$$ is

Let V$$_r$$ denote the sum of the first r terms of an arithmetic progression (A.P.) whose first term is r and the common difference is ($$2r-1$$). Let $${T_r} = {V_{r + 1}} - {V_r} - 2$$ and $${Q_r} = {T_{r + 1}} - {T_r}$$ for r = 1, 2, ...

T$$_r$$ is always