AP EAMCET · Maths · Sequences and Series
The sum of first \(n\) terms of the series \(\frac{3}{5}+\frac{21}{25}+\frac{117}{125}+\ldots\) is
- A \(n+\frac{2^{n+1}}{3 \times 5^n}-\frac{2}{3}\)
- B \(n-\frac{2^{n+1}}{3 \times 5^n}-\frac{2}{3}\)
- C \(n+\frac{2^{n+1}}{3 \times 5^n}+\frac{2}{3}\)
- D \(n-\frac{2^{n+1}}{3 \times 5^n}+\frac{2}{3}\)
Answer & Solution
Correct Answer
(A) \(n+\frac{2^{n+1}}{3 \times 5^n}-\frac{2}{3}\)
Step-by-step Solution
Detailed explanation
Given, series \[ \begin{aligned} & \frac{3}{5}+\frac{21}{25}+\frac{117}{125}+\ldots+\text { upto } n \text { terms } \\ & =\left(1-\frac{2}{5}\right)+\left(1-\frac{4}{25}\right)+\left(1-\frac{8}{125}\right)+\ldots+\text { upto } \end{aligned} \] \(n\) terms…
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