let f_n (t)=t^(n−1) sin(nθ) with t from[0,1[ and θ from [0,π[ 1) prove the uniform convergence of Σ f_n (t) on [0,1[ 2) let S(t)=Σ f_n (t) calculate ∫


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

$l e t f_{n} (t) = t^{n - 1} s i n (n θ) w i t h t f r o m [0, 1 [a n d θ f r o m [0, π [$ $1) p r o v e t h e u n i f o r m c o n v e r g e n c e o f Σ f_{n} (t) o n [0, 1 [$ $2) l e t S (t) = Σ f_{n} (t) c a l c u l a t e \int_{0}^{1} S (t) d t .$
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