COMEDK · Maths · 5. Sequences and Series
The sum of \(n\) terms of the series, \(\dfrac{4}{3}+\dfrac{10}{9}+\dfrac{28}{27}+\ldots\) is
- A \(\dfrac{3^n(2 n+1)+1}{2\left(3^n\right)}\)
- B \(\dfrac{3^n n-1}{2\left(3^n\right)}\)
- C \(\dfrac{3^n(2 n+1)-1}{2\left(3^n\right)}\)
- D \(\dfrac{3^n-1}{2}\)
Answer & Solution
Correct Answer
(C) \(\dfrac{3^n(2 n+1)-1}{2\left(3^n\right)}\)
Step-by-step Solution
Detailed explanation
The given series is \(\dfrac{4}{3} + \dfrac{10}{9} + \dfrac{28}{27} + \ldots + a_n\). The \(n\)-th term \(a_n\) can be written as \(\dfrac{3^n + 1}{3^n} = 1 + \dfrac{1}{3^n} = 1 + 3^{-n}\). The sum of \(n\) terms is…
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