CAPE TOWN, South Africa - President Obama today urged South Africa's youth to continue the fight for equality and opportunity, as he challenged them to live up to the legacy of ailing civil rights icon Nelson Mandela.

"Nelson Mandela showed us that one man's courage can move the world. And he calls on us to make choices that reflect not our fears, but our hopes - in our own lives, and in the lives of our communities and our countries," the president told a crowd of more than 1,000 at the University of Cape Town.

Echoing Robert Kennedy's 1966 "Ripple of Hope" speech at the same location, Obama told students that every voice can make a difference.

"Think of how many ripples of hope it took to build a wave that would eventually come crashing down like a mighty stream," he said. "If there's any country in the world that shows the power of human beings to affect change, this is the one. You've shown us how a prisoner can become a president. You've shown us how bitter adversaries can reconcile. You've confronted crimes of hatred and intolerance with truth and love, and you wrote into your constitution the human rights that sustain freedom."

The president argued that progress in Africa "rests on a fragile foundation" and encouraged the next generation to turn away from handouts from foreign governments in favor of legitimate partnerships that can advance the interests of the continent.

"I can promise you this: The world will be watching what decisions you make. The world will be watching what you do. Because one of the wonderful things that's happening is, where people used to only see suffering and conflict in Africa, suddenly, now they're seeing opportunity for resources, for investment, for partnership, for influence," he said.

"My bet is on the young people who are the heartbeat of Africa's story. I'm betting on all of you. As President of the United States, I believe that my own nation will benefit enormously if you reach your full potential," he said. "I'm calling for America to up our game when it comes to Africa."

As part of that effort, the president announced a new initiative to double access to power in sub-Saharan Africa with an initial $7 billion investment from the U.S.

"It's the lifeline for families to meet their most basic needs. And it's the connection that's needed to plug Africa into the grid of the global economy," he said. "You've got to have power."

The keynote speech of the president's week-long trip to Africa followed a family visit to Robben Island. While the president toured the prison where Mandela spent 18 of his 27 years in captivity in 2006, today, his wife and daughters saw it for the first time.

"There was something different about bringing my children," he said. "Malia is now 15, Sasha is 12 and seeing them stand within the walls that once surrounded Nelson Mandela, I knew this was an experience that they would never forget. I knew that they now appreciated a little bit more the sacrifices that Madiba and others had made for freedom."

"What I also know is that because they've had a chance to visit South Africa for a second time now, they also understand that Mandela's spirit could never be imprisoned - for his legacy is here for all to see. It's in this auditorium: young people, black, white, Indian, everything in between living and learning together in a South Africa that is free and at peace," he said.