GATE BT 2025 | Question: 49

Question

Let $a_{0}=0$ and define $a_{n}=\frac{1}{2}\left(1+a_{n-1}\right)$ for all positive integers $n \geq 1$. The least value of $n$ for which $\left|1-a_{n}\right|<\frac{1}{2^{10}}$ is $\_\_\_\_\_\_$ (Answer in integer)