Other Series

 

We define

 

 

Setting

 

, then

 

 or

 

.

 

Its summation notation is

 

 

Multiplying both sides of above equation by ,

 

 

Therefore,

 

 

 

We thus obtain a remarkable formula that shows the connection to Euler Constant, Sum of Power, and Zeta function.

 

, where .

    

      Or