The string of a helium balloon slips from your hand, and the balloon rises up into the air. When this happens  the balloon rises continually but slows down due to the effect of viscosity.   the balloon rises until it reaches an altitude where its weight equals that of the same volume of air.   the balloon rises until it reaches an altitude where the air and helium densities are equal.   the balloon rises indefinitely because helium is lighter than air.

The correct answer is: the balloon rises until it reaches an altitude where its weight equals that of the same volume of air.

Here's why:

A helium balloon rises because the helium inside the balloon is less dense than the surrounding air. This creates a buoyant force that lifts the balloon upwards.

As the balloon rises, the air pressure decreases. This causes the helium inside the balloon to expand. The balloon will continue to rise until the weight of the displaced air is equal to the weight of the balloon.

At this point, the buoyant force (which is equal to the weight of the air displaced by the balloon) is equal to the weight of the balloon (which includes the weight of the helium inside the balloon and the weight of the balloon material itself).

When these two forces are equal, the balloon is in equilibrium and it stops rising. This happens at an altitude where the weight of the balloon equals the weight of the same volume of air.

So, the balloon does not rise indefinitely, nor does it rise until the air and helium densities are equal. The effect of viscosity would slow down the balloon's ascent, but it is not the primary reason the balloon stops rising.