let-f-n-t-t-n-1-sin-n-with-t-from-0-1-and-from-0-pi-1-prove-the-uniform-convergence-of-f-n-t-on-0-1-2-let-S-t-f-n-t-calculate-0-1-S-t-dt-

Question Number 48009 by maxmathsup by imad last updated on 18/Nov/18

l e t f_{n} (t) = t^{n - 1} s i n (n θ) w i t h t f r o m [0, 1 [a n d θ f r o m [0, π [

1) p r o v e t h e u n i f o r m c o n v e r g e n c e o f Σ f_{n} (t) o n [0, 1 [

2) l e t S (t) = Σ f_{n} (t) c a l c u l a t e \int_{0}^{1} S (t) d t .