let-S-n-k-0-n-1-k-2k-1-1-give-S-n-interms-of-H-n-2-find-lim-n-S-n-3-let-W-n-k-0-n-1-k-4k-2-1-find-W-n-interms-of-H-n-calculate-lim-n-W-n-

Question Number 40047 by abdo mathsup 649 cc last updated on 15/Jul/18

l e t S_{n} = \sum_{k = 0}^{n} \frac{{(- 1)}^{k}}{2 k + 1}

1) g i v e S_{n} i n t e r m s o f H_{n}

2) f i n d {l i m}_{n \to + \infty} S_{n}

3) l e t W_{n} = \sum_{k = 0}^{n} \frac{{(- 1)}^{k}}{4 k^{2} - 1}

f i n d W_{n} i n t e r m s o f H_{n}

c a l c u l a t e {l i m}_{n \to + \infty} W_{n}