Problem 183 (difficulty: 5/10)

Suppose that \(\displaystyle a_nb_n\to 1\), \(\displaystyle a_n+b_n\to 2\). Does it imply that \(\displaystyle a_n\to 1\), \(\displaystyle b_n\to 1\)?

Give me another random problem!

Subject, section:
Requested difficulty:
Request for a concrete problem:I want problem no.

Supported by the Higher Education Restructuring Fund allocated to ELTE by the Hungarian Government