Limits, Continuity & Differentiability · Sandwich theorem with greatest integer

Let

[\cdot]

denote the greatest integer function and

f(x) = \displaystyle\lim_{n\to\infty}\frac{1}{n^3}\sum_{k=1}^{n}\left[\frac{k^2}{3^x}\right]

. Then

12\displaystyle\sum_{j=1}^{\infty} f(j)

is equal to .

Video solution coming soon

We're animating every PYQ step by step. Subscribe to get them first.