[tex]f:\mathbb{R}\to\mathbb{R},\,\,\,f(x) =2x+1\\[/tex]
[tex]\\\begin{aligned} N &= f(0)+f(1)+...+f(10) \\ &= \sum\limits_{x=0}^{10}f(x)\\ &=\sum\limits_{x=0}^{10}(2x+1)\\ &=2 \sum\limits_{x=0}^{10}x+ \sum\limits_{x=0}^{10}1\\ &=2\cdot\dfrac{10\cdot (10+1)}{2}+11\\ &= 10\cdot 11+11\\&=11\cdot(10+1) \\ &=11\cdot 11\\ &=11^2\end{aligned}[/tex]
