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# Masha Lethal Pressure Crush Fetish Mouse

## Masha Lethal Pressure Crush Fetish Mouse

Masha Lethal Pressure Crush Fetish Mouse

The graphics quality is a bit on the low side but the lighting effects are great and the storyline, moral, umm, whatever you want to call it, is great and sets this story apart from the rest.Q: Prove that $2^{n+1}|2^n+1$ for all $n \in \mathbb{N}$ by induction Prove that $2^{n+1}|2^n+1$ for all $n \in \mathbb{N}$ by induction. I tried to use the following step: $2^n+1 = 2^n\cdot 2-2^n$ And then using the inductive hypothesis to solve the smaller problem at the right: $2^{n+1} = 2\cdot2^n$ But I can’t seem to be able to move past this point. A: If $n=1$, your equation is obviously true, as $2^{n+1}=4>2=2^1+1$. Assume that $2^m\mid 2^n+1$ for all $m\leq n$. Then \begin{align*}2^{n+1}+1&=2^{n+1}+2^n\\&=2^{n+1}+2^n+2^n-1\\&=2^{n+1}+2^n-1+2^n+1\\&=2^n+2^{n+1}-1+2^n\\&=2^n+2^n-1+2^n+1\\&=2^{n+1}+1\end{align*} A: Using $2^{n+1}=2(2^n)$ we can simplify to $2^{n+1}+1 = 2^{n+1}+1$ Using $2^n+1=2^n+2^n-2^n$ we can simplify to $2^{n+1}+1 = 2^{n+1}+2^n-2^n$ $2^{n+1}+1= 2^{n+1}+2^n-2^n+2^n$ \$2^{