Question

A=[lg1]+[lg2]+[lg3]+…+[lg2012]

Answer 1

$\it lgx<1,\ \forall x\in\mathbb{N}^*,\ x\leq9\\ \\ 1\leq lgx<2,\ \forall x\in\mathbb{N}^*,\ 10\leq x\leq99\\ \\ 2\leq lgx<3,\ \forall x\in\mathbb{N}^*,\ 100\leq x\leq999\\ \\ 3\leq lgx<4,\ \forall x\in\mathbb{N}^*,\ 1000\leq x\leq2012$

$\it A=\underbrace{0+0+0+\ ...\ +0}_{9\ termeni}+\underbrace{1+1+1+\ ...\ +1}_{90\ termeni}+\underbrace{2+2+2+\ ...\ +2}_{990\ termeni}+\underbrace{ 3+3+3+\ ...\ +3}_{1013\ termeni}=\\ \\ \\ =90+2\cdot990+3\cdot1013=$