Learn Danish: Nogen synger i parken. - Someone is singing in the park.

Danish does not have an exact match for the English "-ing" form. The present tense verb synger translates to both "sings" and "is singing". You do not need an extra "is" in Danish.

Why use nogen here instead of noget or nogle?

Nogen is used for people and means "someone" or "anyone". Noget is used for things meaning "something", and nogle is used for plurals meaning "some". Because an unknown person is singing, nogen is the correct choice.

Where is the word for "the" in i parken?

In Danish, "the" is normally added to the end of the noun instead of being a separate word before it. The word for "a park" is en park. To say "the park", you attach that -en to the end, making it parken.