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If m >1,n in N show that 1m+2m+2^(2m)+2...

If `m >1,n in N` show that `1m+2m+2^(2m)+2^(3m)++2^(n m-m)> n^(i-m)(2^n-1)^mdot`

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Since `m gt 1`, A.M of mth power `gt` mth power of A.M
`(1^(m) + 2^(m) + 4^(m) + 8^(m) + ……+ (2^(n - 1))^(m))/(n) gt ((1 + 2 + 4 + … 2^(n + 1))/(n))^(m)`
`implies 1^(m) + 2^(m) + 4^(m) + …. + 2^((n - 1)m) gt n ((2^(n) - 1)/(n))^(m)`
`= n^(1 - m) (2^(n) - 1)^(m)`
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