It’s a glimmer of hope. By 2040, experts predict, a half-billion sub-Saharan inhabitants still won’t have electricity as power grids remain out of reach. But startups are rewriting that history, taking advantage of more affordable and efficient photovoltaic generation — and a surplus of sunshine. For $13 down and $8 a month — paid wirelessly — Tanzania-based Off-Grid Electric provides a solar panel, battery, phone charger, LED lights and a radio. It might not run freezers, but it’s gradually connecting remotest Africa to the empowered world.