[Solved] Give an example of 2 sequences a_n and b_n such that; a - a_n and b_n are divergent, but a_n+b_n is convergent b- a_n is convergent, b_n is divergent,
Question: Give an example of 2 sequences \(\left\{ {{a}_{n}} \right\}\) and \(\left\{ {{b}_{n}} \right\}\) such that;
a - \(\left\{ {{a}_{n}} \right\}\) and \(\left\{ {{b}_{n}} \right\}\) are divergent, but \(\left\{ {{a}_{n}}+{{b}_{n}} \right\}\) is convergent
b- \(\left\{ {{a}_{n}} \right\}\) is convergent, \(\left\{ {{b}_{n}} \right\}\) is divergent, and \(\left\{ {{a}_{n}}{{b}_{n}} \right\}\) is divergent
c- \(\left\{ {{a}_{n}} \right\}\) is divergent, and \(\left\{ \left| {{a}_{n}} \right| \right\}\) is convergent
Deliverable: Word Document 