JEE Main 202621 Jan, Evening shiftMathematicsMediumIntegral Calculus369× since 2002Let [⋅][\cdot][⋅] denote the greatest integer function and f(x)=limn→∞1n3∑k=1n[k23x]f(x)=\lim_{n\to\infty}\frac{1}{n^3}\sum_{k=1}^{n}\left[\frac{k^2}{3^x}\right]f(x)=limn→∞n31∑k=1n[3xk2]. Then 12∑j=1∞f(j)12\sum_{j=1}^{\infty}f(j)12∑j=1∞f(j) is equal to ______.Your answerType your answer. Integers and decimals are accepted.CheckSkip · show solution
