Question

Помогите Срочно плиз (a+2a+3a+...+na)/(n^2-2n-3)-3a/(2(n-3))

Answer 1

a + 2a + 3a + 4a +  ... + na = a·(1+2+3+4+ ... + n)=a·(1+n)·n/2

n²-2n-3=0
D=(-2)²-4·(-3)=4+12=16
n₁=(2-4)/2=-1    или       n₂=(2+4)/2=3
n²-2n-3=(n+1)(n-3)


$frac{a+2a+3a+...+na}{n^2-2n-3}- frac{3a}{2(n-3)} = \ \ =frac{a+2a+3a+...+na}{n^2-2n-3}- frac{3a}{2(n-3)} =frac{acdot frac{(1+n)cdot n}{2} }{(n+1)(n-3)}- frac{3a}{2(n-3)} = \ \ =frac{acdot n}{2cdot(n-3)}- frac{3a}{2(n-3)} = \ \ = frac{an-3a}{2cdot(n-3)}= frac{acdot(n-3)}{2cdot(n-3)}= frac{a}{2}$