I have been given a rearrangement of the alternating harmonic series that follows the following arrangement:
$\dfrac{1}{1}$$-$$\dfrac{1}{2}$$-$$\dfrac{1}{4}$$-$$\dfrac{1}{6}$$+$$\dfrac{1}{3}$$-$$\dfrac{1}{8}$$-$$\dfrac{1}{10}$$-$$\dfrac{1}{12}$$+$...
And been told to consider that if you bracket terms in fours, the $nth$ bracket is:
($\dfrac{1}{(2n-1)}$$-$$\dfrac{1}{(6n-4)}$$-$$\dfrac{1}{(6n-2)}$$-$$\dfrac{1}{6n}$)
Finally I have been asked to first show that the bracketed series converges and that, secondly, the original series converges
Any help at all would be appreciated thanks.