let-S-n-x-k-0-n-e-k-sin-k-2-x-1-determine-2-sequence-U-n-x-and-V-n-x-wich-verify-U-n-S-n-V-n-2-let-S-lim-n-S-x-study-the-convergence-of-S-

Question Number 63651 by mathmax by abdo last updated on 06/Jul/19

l e t S_{n} (x) = \sum_{k = 0}^{n} e^{- k} s i n (k^{2} x)

1) d e t e r m i n e 2 s e q u e n c e U_{n} (x) a n d V_{n} (x) w i c h v e r i f y U_{n} ⩽ S_{n} ⩽ V_{n}

2) l e t S = {l i m}_{n \to + \infty} S (x) s t u d y t h e c o n v e r g e n c e o f S .