Problem

Identify the correct statement. a.

\lim_{n \to \infty} \left[ \sum_{r=1}^{n} \frac{1}{2^r} \right] = 1

b. If

f(x) = (x-1)\{x\}

, where

[ \cdot ]

and

\{ \cdot \}

denotes greatest integer function and fractional part of

x

respectively, the limit of

f(x)

does not exist at

x=1

\lim_{x \to 0^+} \left[ \frac{\tan x}{x} \right] = 1

\left[ \lim_{x \to 0^+} \frac{\tan x}{x} \right] = 1