Where did Philo Farnsworth invent the first televion?

Farnsworth didn't invent the television.

John Logie Baird demonstrated his television to the public in March 1925 at Selfridges department store in London. He called it the Televisor and it was Baird's system that was used by the BBC to start television broadcasts in 1929.

Philo Farnsworth demonstrated his in 1928, three years later.

Both Baird's and Farnsworth's televisions were electro-mechanical, that is they had moving parts that were required to create an image.

However, Farsnworth is credited with the worlds first fully electronic television, shown off in 1929. This model eliminate all moving parts and was a step towards higher definition television. His electronic system was put into service in the US in 1939.