let-f-t-n-1-1-n-ln-1-t-2-n-1-t-2-1-study-the-simple-and-uniform-convergence-of-f-n-2-study-the-continuity-of-f-3-prove-that-lim-t-f-t-ln-2-pi-

Question Number 36750 by prof Abdo imad last updated on 05/Jun/18

l e t f (t) = \sum_{n ⩾ 1} {(- 1)}^{n} l n {1 + \frac{t^{2}}{n (1 + t^{2})}}

1) s t u d y t h e s i m p l e a n d u n i f o r m c o n v e r g e n c e

o f Σ f_{n}

2) s t u d y t h e c o n t i n u i t y o f f

3) p r o v e t h a t {l i m}_{t \to + \infty} f (t) = l n (\frac{2}{π}) .