let-S-n-k-1-1-k-1-k-and-T-n-k-1-1-k-1-2k-1-1-calculate-lim-S-n-and-lim-T-n-n-2-prove-that-S-n-ln2-and-T-n-pi-4-converges-and-find-its-sum-

Question Number 33348 by caravan msup abdo. last updated on 14/Apr/18

l e t S_{n} = \sum_{k = 1}^{\infty} \frac{{(- 1)}^{k - 1}}{k} a n d

\underset{n}{T} = \sum_{k = 1}^{\infty} \frac{{(- 1)}^{k - 1}}{2 k - 1}

1) c a l c u l a t e l i m S_{n} a n d l i m T_{n} (n \to \infty)

2) p r o v e t h a t Σ (S_{n} - l n 2) a n d

Σ (T_{n} - \frac{π}{4}) c o n v e r g e s a n d f i n d i t s s u m