calculate-A-n-0-dx-x-1-x-2-x-n-n-integr-2-

Question Number 34277 by math khazana by abdo last updated on 03/May/18

c a l c u l a t e A_{n} = \int_{0}^{\infty} \frac{d x}{(x + 1) (x + 2) \dots . (x + n)}

n i n t e g r ⩾ 2 .

Commented by candre last updated on 03/May/18

\frac{1}{\underset{i = 1}{\prod^{n}} (x + i)} = \underset{i = 1}{\sum^{n}} \frac{C_{i}}{x + i}

1 = \underset{j = 1}{\sum^{n}} C_{j} \underset{i = 1 \land i \neq j}{\prod^{n}} (x + i)

x = - j \Rightarrow 1 = C_{j} \underset{i = 1 \land i \neq j}{\prod^{n}} (i - j)

Facebook Tweet Pin