Other Series
Other Series
Define
,
where i, k and n are positive integers.
Setting
,
Then, as n approaches infinity, we have
or
.
The above series is expressed in the summation notation as
.
Multiplying both sides of above sum by 
gives
gives
.
Therefore, we obtain
.
We thus obtain a remarkable formula that shows the connection to Euler Constant, sums of power, and Zeta function.
,
where 
.
.
Notice that
, where A is Glaisher’s constant = 1.28243…