let S_n = Σ_(k=1) ^∞ (((−1)^(k−1) )/k) and T_n = Σ_(k=1) ^∞ (((−1)^(k−1) )/(2k−1)) 1) calculate lim S_n and lim T_n (n→∞) 2)prove that Σ(S_n −ln2) and Σ(T


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

$l e t S_{n} = \sum_{k = 1}^{\infty} \frac{{(- 1)}^{k - 1}}{k} a n d$ $\underset{n}{T} = \sum_{k = 1}^{\infty} \frac{{(- 1)}^{k - 1}}{2 k - 1}$ $1) c a l c u l a t e l i m S_{n} a n d l i m T_{n} (n \to \infty)$ $2) p r o v e t h a t Σ (S_{n} - l n 2) a n d$ $Σ (T_{n} - \frac{π}{4}) c o n v e r g e s a n d f i n d i t s s u m$
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