Demonstration of sequences: Prove why sum of converging seq. and pos. diverging seq. is pos. diverging

[Crescenzo2003]

Demonstrate (algebraic proof) why the sum sequence (C_n) made of a converging sequence (a_n) plus a positively diverging sequence (b_n) is positively diverging

C_n = a_n + b_b
(a_n convergin sequence, b_n positively diverging sequence)
(demonestrate why c_n is also positively diverging)

Thank you in advance, sorry for the bad english it is not my first language.

 

[stapel]

Demonstrate (algebraic proof) why the sum sequence (C_n) made of a converging sequence (a_n) plus a positively diverging sequence (b_n) is positively diverging

C_n = a_n + b_n
(a_n convergin sequence, b_n positively diverging sequence)
(demonestrate why c_n is also positively diverging)

What are your thoughts? What have you tried? How far have you gotten?

Please be complete. Thank you!

Eliz.