Limiting magnitudes for different telescopes I live in an extremely light polluted place. On a new moon night,  magnitude 3.5 stars are at the limit of  naked eye visiblity on clear nights, and the Orion nebula is visible as a smudge through my binoculars and I can see 6-7 stars of the Pleaidies (apparent magnitude about 5.5 I guess)
If I buy a 130 mm reflector telescope, roughly what will be the limiting magnitude of the objects I can see?
I used $5log(130/6.5)=6.5$, which means I would be able to see upto about magnitude 10 even from a light polluted city.
This sounds too good to be true...
Is my estimate roughly accurate and do you think spending a few hundred dollars on the telescope is worth it if I never intend to leave the city for a while?
Your calculated estimate may be about correct for the limiting magnitude of stars, but lots of what you might want to see through a telescope consists of extended objects-- galaxies, nebulae, and unresolved clusters.  The magnitude estimates of these objects tend to consider them as point sources, but as extended objects they have much less of a contrast difference with the sky.  In my experience in an equally light-polluted location with a similar-size telescope, the sky brightness makes the limiting magnitude of extended objects between 7 and 8, even with a light-pollution reduction filter in use.
That isn't to say a telescope is worthless in the city; you can still observe the Moon and planets, resolved clusters are pretty, and you can observer the brighter extended objects.  But bringing the telescope to a dark-sky location makes an incredible difference with many more objects visible.