Take note that an alternating series
`sum` `a_n = sum (-1)^(n+1) b_n`
is convergent if the following conditions are satisfied.
(i) `b_n` is decreasing, and
(ii) ` lim_(n->oo) b_n=0` .
In the given alternating series, the bn is:
`b_n = 1/(n+1)`
Then, check if the values of bn decrease as n increases by 1.
`n=1` , `b_n = 1/2`
`n=2` , `b_n=1/3`
`n=3` , `b_n=1/4`
`n=4` , `b_n=1/5`
So bn is decreasing.
Also, take the limit of bn as n approaches infinity.
`lim_(n->oo) b_n = lim_(n->oo) 1/(n+1) = 0`
Since the result is zero, the second condition is satisfied too.
Therefore, by Alternating Series Test, the given series is convergent.