Question

If n = 2020, evaluate 1/log base2 n + 1/log base3 n + … + 1/log base2019 n?

Answer 1

log2(base n) + log3(base n) +...+ log2019(base n)

= log1*2*3*4*5*...*2019(base n)

= log2019!(base n)

= log2019!(base 2020!)

= log2020!/2020(base 2020!)

= log2020!(base 2020!) - log2020(base 2020!)

= 1 - log2020(base 2020!)

= 1 - log2020(base n)