Does the following infinite series converge or diverge? explain your answer. 1/2 - 2/9 + 4/27 - 8/81

Something tells me the first term is supposed to be , not . In that case, the series would be



which is geometric with a ratio less than 1, so the infinite series will converge, and moreover will converge to



Even if the first term was , the series will still converge, but we can't write it as we did above. Not counting the first term, we still have a convergent geometric series.