Limit: $\lim_{n \to \infty} \frac{3^n+5^n+10^n}{-2^{n+1}+5^{n+1}+10^{n+1}}$ Limit: $$\lim_{n \to \infty} \frac{3^n+5^n+10^n}{-2^{n+1}+5^{n+1}+10^{n+1}}$$
I know the limit is $\frac{1}{10}$, but I am not sure how to get to it. Any help would be greatly appreciated.

$$\lim _{ n\to \infty  } \frac { 3^{ n }+5^{ n }+10^{ n } }{ -2^{ n+1 }+5^{ n+1 }+10^{ n+1 } } =\lim _{ n\to \infty  } \frac { { 10 }^{ n }\left( \frac { { 3 }^{ n } }{ { 10 }^{ n } } +\frac { { 5 }^{ n } }{ { 10 }^{ n } } +1 \right)  }{ { 10 }^{ n+1 }\left( -\frac { { 2 }^{ n+1 } }{ { 10 }^{ n+1 } } +\frac { { 5 }^{ n+1 } }{ { 10 }^{ n+1 } } +1 \right)  } =\\ ==\lim _{ n\to \infty  } \frac { { \left( \frac { 2 }{ 10 }  \right)  }^{ n }+{ \left( \frac { 5 }{ 10 }  \right)  }^{ n }+1 }{ { 10 }\left( { -\left( \frac { 2 }{ 10 }  \right)  }^{ n+1 }+{ \left( \frac { 5 }{ 10 }  \right)  }^{ n+1 }+1 \right)  } =\frac { 1 }{ 10 } $$
