Seems Easy?

Number Theory Level 3

Consider the set\(A\) of numbers \({1,\frac{1}{2},\frac{1}{3},.....,\frac{1}{2012}}\) . We delete two of them say \(a\) and \(b\) and in their place we put only one number \(a+b+ab\). After performing the operation 2011 times what is the number that is left over.

Note- It's an old NMTC Junior level problem

Excel in math and science

Master concepts by solving fun, challenging problems.

It's hard to learn from lectures and videos

Learn more effectively through short, conceptual quizzes.

Our wiki is made for math and science

Master advanced concepts through explanations, examples, and problems from the community.

Used and loved by 4 million people

Learn from a vibrant community of students and enthusiasts, including olympiad champions, researchers, and professionals.