JEE Mains · Maths · STD 11 - 8. sequence and series
Let \(f\) be a polynomial function such that \(\log_2(f(x)) = \left(\log_2\left(2+\dfrac{2}{3}+\dfrac{2}{9}+\ldots\infty\right)\right)\cdot\log_3\left(1+\dfrac{f(x)}{f(1/x)}\right)\), \(x>0\) and \(f(6)=37\). Then \(\displaystyle\sum_{n=1}^{10}f(n)\) is equal to ________.
- A 385
- B 390
- C 395
- D 400
Answer & Solution
Correct Answer
(C) 395
Step-by-step Solution
Detailed explanation
The sum of the infinite geometric progression is given by: \(S = 2 + \dfrac{2}{3} + \dfrac{2}{9} + \ldots \infty = \dfrac{2}{1 - \dfrac{1}{3}} = 3\) Substituting this into the given equation: \(\log_2(f(x)) = \log_2(3) \cdot \log_3\left(1 + \dfrac{f(x)}{f(1/x)}\right)\) Using…
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