Explanation

(b)
$\frac{4}{3} + \frac{10}{9} + \frac{28}{27} + ...$upto $n$ terms
=$\left( 1 + \frac{1}{3} \right) + \left( 1 + \frac{1}{9} \right) + \left( 1 + \frac{1}{27} \right) + ...$upto $n$ terms
$= (1 + 1 + 1 + ...n\ terms) + \left( \frac{1}{3} + \frac{1}{3^{2}} + \frac{1}{3^{3}} + ...n\ terms \right)$
$= n + \frac{1}{3}\left( \frac{1 - \frac{1}{3^{n}}}{1 - \frac{1}{3}} \right) = \frac{3^{n}(2n + 1) - 1}{2(3^{n})}$