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If ngt1 then prove that 1/(log2 n )+1/(l...

If `ngt1` then prove that `1/(log_2 n )+1/(log_3 n)+.................+1/log_(53) n =1/(log_(53!) n`

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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