Final answer:
The parallax of the closest stars was not observed until 200 years after the invention of the telescope because the parallax effect is extremely subtle and the necessary precision instruments to detect it were not developed until the 18th century.
Step-by-step explanation:
The reason why the parallax of the closest stars was not observed until 200 years after the invention of the telescope is due to the extremely small shift in the star's position that is caused by parallax. Early astronomers did not possess the technology to measure these minute shifts, as the tools required to detect parallax shifts too small for the human eye did not exist. Moreover, the stars are significantly more distant than originally believed, which contributed to the already minute shifts caused by parallax being even smaller than expected.
It took until the 18th century for astronomers to develop the necessary instruments capable of measuring these tiny displacements with enough precision to confirm Earth's revolution around the Sun. In 1838, astronomers like Friedrich Bessel, Thomas Henderson, and Friedrich Struve finally succeeded in measuring the parallax of nearby stars such as 61 Cygni, Alpha Centauri, and Vega.