Your sum has no limits, so I'm assuming an infinite series starting at n = 0. Notice this is an alternating series with the magnitude of the terms decreasing to 0 as n goes to infinity. So the series converges and you know the value of a partial sum with m term differs from the value of the series by at most the magnitude of the (m+1)st term. With your calculator you find that the magnitude of the 3nd term is of the order of E-28. So just the sum of the 1st two terms is very close to the true value. I find the answer you gave to be correct.