TRUE OR FALSE give an explanation If 1n1 an is an alternatin

TRUE OR FALSE: (give an explanation)

If (-1)n+1 an is an alternating series that satisfies the conditions of the alternating series test, then the series an also

Solution

False. A alternating series converges if the terms get smaller and approach infinity. This is not true for a non-alternating series (harmonic series 1/n diverges).