Statement -1: If a,b,c are distinct real numbers in H.P, then `a^(n)+c^(n)gt2b^(n)" for all "ninN`.
Statement -2: `AMgtGMgtHM`

Explanation

`therefore GgtH`
`therefore sqrt(ac)gtb`
`implies (ac)^((n)/(2))gtb^(n) " or " a^((n)/(2))c^((n)/(2))gtb^(n) " " "....(i)"`
Also, `(a^((n)/(2))-c^((n)/(2)))^(2)gt0 implies a^(n)+c^(n)-2a^((n)/(2))c^((n)/(2))gt0`
`implies a^(n)+c^(n)gt2a^((n)/(2))c^((n)/(2))gt2b^(n)" " [" from Eq.(i) "]"....(i)"`
`therefore a^(n)+c^(n)gt2b^(n)`