1.001^1000 to nearest tenth.

Rachel is standing at the middle of a 3 by 3 square grid. Every second, she randomly chooses to walk up, down, left, or right by 1 unit. Rachel stops if she walks outside the square. Find the the expected value of (in other words, on average) the number of steps she makes before she stops. (For example, if she goes left two times, she stops, and the number of steps made is 2)

Rollingblade
Oct 28, 2018

#1**+2 **

1. The expression can be re-written as \((1+\frac1{1000})^{1000}\). Since Euler's constant, \(e\), is equilavent to \((1+\frac1n)^n\) when \(n\) approches infinity. Therefore, the expression is approimately \(e=2.717\cdots\).

2. \(\frac92\) (I'll add the solution if I have time).

GYanggg
Oct 28, 2018