The tech-heavy Nasdaq recovered after earlier taking a hit by a slide in Tesla Inc TSLA.O and other megacap stocks. By Chris Prentice and Amanda Cooper WASHINGTON/LONDON, Oct 24 (Reuters) - U.S. and European shares rose on Monday as signs of a cooling U.S. economy raised hopes that the Federal Reserve will slow its pace of rate hikes. U.S. business activity contracted for a fourth straight month in October, a survey showed, in the latest evidence of an economy softening in the face of high inflation and rising interest rates.