Let $f:\mathbb R \rightarrow \mathbb R$ be a non-constant, thrice differentiable function such that $f(1+1/n)=1$ for all $n \in \mathbb Z$. then what is the value of $f^{\prime \prime}(1)$? [![enter image description here](https://i.stack.imgur.com/nI4Ll.jpg)](https://i.stack.imgur.com/nI4Ll.jpg)

Answer is 0