let-consider-the-serie-n-1-sin-1-n-x-n-1-find-the-radius-of-convergence-2-study-the-convergence-at-R-and-R-3-let-S-x-its-sum-study-the-continuity-of-S-4-prove-that-1-x-x-1-S-x-0-

Question Number 33359 by caravan msup abdo. last updated on 15/Apr/18

l e t c o n s i d e r t h e s e r i e \sum_{n ⩾ 1} s i n (\frac{1}{\sqrt{n}}) x^{n}

1) 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

2) s t u d y t h e c o n v e r g e n c e a t - R a n d R

3) l e t S (x) i t s s u m s t u d y t h e c o n t i n u i t y

o f S

4) p r o v e t h a t {(1 - x)}_{x \to 1^{-}} S (x) \to 0