Answer 1

If we need the sum upto n terms, one way to do it in linear time would be like this:

res = 1/2 ;
for(int i = 1; i < n; i++)
{
if( ¡&1)
res+= (2*i+1)/(2*i+2);
else
res-= (2*i+1)/(2*i+2);
}
return res;