Let f be a polynomial function such that log ₂(f(x))=(log ₂(2+2/3+2/9+ ∞))· log ₃(1+(f(x))/(f(1/x))), x>0 and f(6)=37. Then Σ n=1 ¹⁰f(n) is equal to _ _ _.

Sets, Relations and Functions: JEE Main 2026 Mathematics question

JEE Main 2026 · 8 Apr, Evening shift · Q25

JEE Main 20268 Apr, Evening shiftMathematicsMediumSets, Relations and Functions168× since 2002

Let

f

be a polynomial function such that

\log_2(f(x))=\left(\log_2\left(2+\frac{2}{3}+\frac{2}{9}+\ldots\ldots\infty\right)\right)\cdot\log_3\left(1+\frac{f(x)}{f\left(\frac{1}{x}\right)}\right)

x>0

and

f(6)=37

. Then

\sum_{n=1}^{10}f(n)

is equal to ______.

Your answerType your answer. Integers and decimals are accepted.