A balloon filled with helium or hydrogen gas keeps on going vertically upward into the sky.
The density of air decreases with altitude thus the balloon filled with helium or hydrogen gas does not rise indefinitely. As the balloon gradually goes up, the weight of the displaced air, which is known as upthrust, decreases. It keeps on rising as long as up thrust exceeds its weight. When upthrust becomes equal to its weight, it stops rising further. Hence the given statement is false.