Billionaire Philip Falcone’s LightSquared Inc. reached a 15-year deal with Sprint Nextel Corp. to share network expansion costs and equipment, and to provide high-speed wireless service to the phone company. Falcone told Harbinger Capital Partners hedge fund investors yesterday about the accord in a letter obtained by Bloomberg News. The companies were discussing a deal valued at as much as $20 billion, people familiar with the matter said earlier this month.