The sum is $\sum_{k=1}^{\infty}\frac{(-1)^{k+1}}{k^2+k}$
Question: Determine this sum with 6 correct decimals. And Estimate the truncation error.
Firstly we know the MATLAB uses double precision, from binary number, we could find the smallest possible number that Matlab could use.
$x_s=m\beta^{e}$, let $e=-1022$, m has at most $52$ digits, then, $x_s=2^{-1074}$
And then, $k^2+k=2^{1074}$, this $k$ is the largest number of terms that Matlab could handle.
But I don't know how to continue.