Give an example of a convergent sequence $\{a_n\}$ and divergent sequence $\{b_n\}$ such that $\{a_n+b_n\}$ is a convergent series.
I've been trying to solve this question for a couple days now and have been struggling, if anyone could give me a hint or show me how you got your answer as I feel this isn't solvable but the question says that I must have an example. Thank you in advance, Math Student 🙂
Best Answer
Assume ${a_n + b_n}$ converges. Since ${a_n}$ converges, ${a_n + b_n - a_n}$ converges, contradicting the fact that ${b_n}$ does not converge.