If a,;b,;c are in H.P., then for all n in N t | vedclass

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Question

(b) For two numbers $a$ and $c$

$\frac{{{a^n} + {c^n}}}{2} > {\left( {\frac{{a + c}}{2}} \right)^n}$ (Where $n \in N,\;n > 1$)

$A.M. >

Vedclass · Accepted Answer

${a^n} + {c^n} > 2{b^n}$

Vedclass · Answer

(b) For two numbers $a$ and $c$

$\frac{{{a^n} + {c^n}}}{2} > {\left( {\frac{{a + c}}{2}} ight)^n}$ (Where $n \in N,\;n > 1$)

$A.M. > G.M. > H.M.$

$	herefore $$\frac{{a + b}}{2} > b$ $(\;a,\;b,\;c$ are in $H.P.$)

$ \Rightarrow $${\left( {\frac{{a + c}}{2}} ight)^n} > {b^n}$

$ \Rightarrow $$\frac{{{a^n} + {c^n}}}{2} > {\left( {\frac{{a + c}}{2}} ight)^n} > {b^n}$.

If $a,\;b,\;c$ are in $H.P.$, then for all $n \in N$ the true statement is

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