Question

The sum of \(n\) terms of the series \(1 + \frac{4}{5} + \frac{7}{5^2} + \frac{10}{5^3} + \dots\) is

• A. \(\frac{5}{4} + \frac{15}{16}\left(1 - \frac{1}{5^{n-1}}\right) - \frac{(3n-2)}{4\cdot 5^{n-1}}\)
• B. \(\frac{5}{4} + \frac{1}{16}\left(1 - \frac{1}{5^{n-1}}\right) - \frac{3n}{4\cdot 5^{n-1}}\)
• C. \(\left(1 - \frac{1}{5^{n-1}}\right) - \frac{(3n+2)}{4\cdot 5^{n-1}}\)
• D. None of the above

Hint:

Arithmetico-geometric series: use \(S_n - rS_n\) method.

Answer 1

The Correct Option is A