A = \(\dfrac{1}{2}+\dfrac{3}{2}+\dfrac{3}{2^2}+\dfrac{3}{2^3}+.....+\dfrac{3}{2^{2021}}+\dfrac{3}{2^{2022}}\)
\(2\times\)A = 1 + 3+ \(\dfrac{3}{2}\) +\(\dfrac{3}{2^2}\) + \(\dfrac{3}{2^3}\)+...........+\(\dfrac{3}{2^{2021}}\)
2 \(\times\) A - A = 4 - \(\dfrac{1}{2}\) - \(\dfrac{3}{2^{2022}}\)
A = \(\dfrac{7}{2}\) - \(\dfrac{3}{2^{2022}}\)
B = 2 \(\times\dfrac{3}{2^{2023}}\)
A - B = \(\dfrac{7}{2}-\dfrac{3}{2^{2022}}\) - 2 \(\times\) \(\dfrac{3}{2^{2023}}\)
A - B = \(\dfrac{7}{2}\) - \(\dfrac{3}{2^{2022}}\) - \(\dfrac{3}{2^{2022}}\)
A - B = \(\dfrac{7}{2}\) - \(\dfrac{6}{2^{2022}}\)
A - B = \(\dfrac{7}{2}\) - \(\dfrac{3}{2^{2021}}\)