Question
Prove that if $\left\{a_{n}\right\}$ converges and $\left\{b_{n}\right\}$ diverges then $\left\{a_{n}+b_{n}\right\}$ diverges.
Step 1
Since $\{a_n\}$ converges, there exists a limit $L_a$ such that for any $\epsilon > 0$, there exists an $N_a$ such that for all $n > N_a$, we have $|a_n - L_a| < \epsilon$. Show more…
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