Euro zone economies are showing signs that the worst recession in six decades is easing.The Purchasing Managers Index – a measure of service and manufacturing activity – rose in May for the third month running. Though still indicating contraction rather than expansion, the index is at its highest level since October last year. In the services sector firms said they were even more optimistic about the future. And the survey of 2,000 companies revealed businesses as a whole had their brightest outlook in nearly a year. Business expectations were the rosiest in 15 months for Spain, and the brightest in 10 months for both Germany and France. They hit an eight-month high in Italy. Economists said the figures give hope that the economy will contract less in the second quarter of this year than it did in the first three months. Recent statistics show the euro zone’s economy shrank 2.5 percent between January and March.