Question

1/3 b = 5/3^2+ 5/3^3+5/3^4+...+5/3^20+5/3^21

Answer 1

\(\Leftrightarrow b=\dfrac{5}{3}+\dfrac{5}{3^2}+...+\dfrac{5}{3^{20}}\)

=>\(3b=5+\dfrac{5}{3}+...+\dfrac{5}{3^{19}}\)

=>\(2b=5-\dfrac{5}{3^{20}}=\dfrac{5\cdot3^{20}-5}{3^{20}}\)

=>\(n=\dfrac{5\cdot3^{20}-5}{3^{20}\cdot2}\)