Let-consider-a-n-n-and-u-n-n-two-reals-sequence-defined-such-as-a-0-1-n-gt-1-a-n-1-p-0-n-a-p-a-n-p-and-p-0-n-a-p-u-n-p-0-Part1-1-Express-n-gt-1-a-n-i

Question Number 68220 by ~ À ® @ 237 ~ last updated on 07/Sep/19

L e t c o n s i d e r {(a_{n})}_{n} a n d {(u_{n})}_{n} t w o r e a l s s e q u e n c e

d e f i n e d s u c h a s a_{0} = 1, \forall n > 1 a_{n + 1} = \underset{p = 0}{\sum^{n}} a_{p} a_{n - p} a n d \underset{p = 0}{\sum^{n}} a_{p} u_{n - p} = 0

P a r t 1

1) E x p r e s s \forall n > 1 a_{n} i n t e r m s o f n

2) F i n d t h e l a r g e s t d o m a i n o f c o n v e r g e n c e o f t h e i n t e g e r s e r i e {a_{n} x^{n}}

3) D e t e r m i n a t e \forall x \in D t h e s u m f (x) o f {a_{n} x^{n}}

4) F i n d t h e r a d i u s o f c o n v e r g e n c e o f t h e s e r i e {u_{n} x^{n}}

5) G i v e t h e r e l a t i o n t h a t b e t w e e n t h e s u m S (x) o f t h e s e c o n d s e r i e a n d \frac{x}{f (x)}

6) C a n y o u d e v e l o p p i n i n t e g e r s e r i e g (x) = \frac{π x}{t a n (π x)}

P a r t 2

N o w d o t h e p a r t 1 b u t i n t h e o r d e r 2) - 1) - 3) - 4) - 5) - 6)