Simplifying this logarithm series ∑ i = 2 99 1 log i ( 99...
Simplifying this logarithm series
How would you evaluate (or at least simplify) this logarithm series?
Answer & Explanation
Note that , for any choice of base of the logarithm. (Mathematicians tend to mean the natural logarithm when they write .)
In particular, .
Therefore your sum is:
where in first equality I used the well-known fact that .