If the product $(x+2)(x+3)(x+4)\cdots(x+9)(x+10)$ expands to $a_9x^9+a_8x^8+\dots+a_1x+a_0$, then what is the value of $a_1+a_3+a_5+a_7+a_9$? 
When expanded, the product $(x+2)(x+3)(x+4)\cdots(x+9)(x+10)$ can be written as $a_9x^9+a_8x^8+\dots+a_1x+a_0$. What is the value of $a_1+a_3+a_5+a_7+a_9$?


On expansion of $$(x+2)(x+3)(x+4)...(x+9)(x+10)$$ we have
$$(x+2)(x+3)(x+4)...(x+9)(x+10) = x^9+54x^8+1186x^7+14084x^6+100045x^5+439850x^4+1182204x^3+1844936x^2+1458720x+403200$$
which is written in the form of  $~~a_9x^9+a_8x^8+...+a_1x+a_0$.
Then, $$a_1+a_3+a_5+a_7+a_9~=~ 1458720~+~1182204~+~100045~+~1186~+~1~=~2742156$$
