Euler says: when (s) tends to infinity, the value of the following expression reaches to:

Euler wanted to prove that SUM and INTEGRALS give different values.

No. It is not so.

As it is well known

The following expression gives these differences:

If (ds=1)               this value=0,577215665…         it confirms Euler

If (ds=0,1)            this value=0,050861..              it does not confirm        

If (ds=0,0….001)  this value=0,00000000000…  it does not confirm

So, a constant “GAMMA” do not exist.

Or, every body may create a constant for him.