This is not true!

Although equality holds for n=1:




It isn't true for n=2 or greater, for when n=2


yet
,  holds but not 

And when n=3


yet
, again  holds but not .

Euler proved in 1735 that the the sum on the left approaches the irrational
number  = 1.6449340668482264... and it is an increasing function, so it
is always less that .

The expression on the right is also increasing, and approaches 2.  But
beginning with the third term it is already larger than the left side can 
ever be!

Edwin