Question 8151
this is the sum of a geometric progression/series with r=-1/2 and starting with a=1/2.


{{{S[alpha] = a/(1-r)}}}

{{{S = (1/2)/(1-(-1/2))}}}
{{{S = (1/2)/(1+(1/2))}}}
{{{S = (1/2)/(3/2)}}}
{{{S = 1/3}}}


then add the original 1, to give a sum of 4/3


jon