Question

Give an example of a convergent sequence X + Y where X converges and Y diverges. Or justify why it cannot be true.

Answer 1

i cnt come up with anything

Answer 2

It can't be true. This is because \(Y_n =(X_n +Y_n )-X_n \), and since both \(X_n +Y_n \) and \(X_n \) are convergent, \(Y_n \) must be as well. The sum/difference of two convergent sequences is also convergent.

Answer 3

That makes sense. Thank you!