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If n >1,then prove that 1/((log)2n)+1/(...

If `n >1`,then prove that `1/((log)_2n)+1/((log)_3n)+.......+1/((log)_(53)n)=1/((log)_(53 !)n)dot`

Text Solution

Verified by Experts

The given expression is equal to
`log_(n) 2+ log_(n) 3 +...+log_(n) 53 = log_(n) (2 xx 3 xx ...xx53)`
` log_(n) 53! = 1/(log_(53!^(n)))`
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